Apparatus for forming color images, using a hue-plus-gray color model

ABSTRACT

The invention is for use with a visible medium capable of light reflection etc., and for use with a color-image source that defines a desired color. Here a device for causing the medium to appear colored includes a gray-scale subsystem to achromatically suppress a stated fraction of the reflection; and at least two device-primary subsystems to cause selective reflection of light of two associated device-primary colors. Even if the device, as originally made, in effect uses the gray-scale subsystem to help construct colors, or the device-primary subsystems to help form gray-scale &#34;values&#34;, such cross-dependency is essentially removed. A programmed processor resolves the desired-rendition information into Fraction-Black, Fraction-Colorant, and hue. Fraction-Black information is applied exclusively to control only the gray-scale subsystem; Fraction-Colorant to control only the device-primary subsystem; and hue to select a dominant and a subordinate primary subsystem and as between them apportion the Fraction-Colorant.

This is a continuation of application Ser. No. 07/878,931, filed on May4, 1992, now U.S. Pat. No. 5,377,024.

RELATED APPLICATION

A related application is Ser. No. 07/878,579, filed on May 4, 1992, inthe names of Jeffrey S. Best and Paul H. Dillinger, and entitled "METHODFOR FORMING COLOR IMAGES, USING A HUE-PLUS-GRAY COLOR MODEL AND ERRORDIFFUSION", attorney docket PD-191063.

MICROFICHE APPENDIX

A microfiche appendix with 254 microfiches in one page is filed withthis application.

BACKGROUND

1. Field of the Invention

This invention relates generally to generation of colors oncolor-reproduction devices--and more particularly to dot-on-dotsheet-medium printing systems, including color-halftone systems.

2. Prior Art

In recent years computer-driven machines have become available forproducing color graphics--diagrams, abstract patterns or pictures--on asheet medium such as paper. Such machines are generally controlled in atwo-step process.

First a user sets up desired colors on a cathode-ray-tube (CRT) display;then the user directs the machine to print the selected colors onto thesheet medium. Both stages of control are found to be very problematic.

In the first stage, sometimes called "color adjustment" or "colorcompensation", although desired colors may be very clearly in mind, theuser struggles with circuitous, seemingly irrational procedures forexpressing to the color system just what those desired colors are.Attempts to operate a conventional color-compensation stage usuallyrange from annoying to quite maddening.

After that difficult, patience-testing step has been satisfactorilycompleted, however, the user encounters new problems in the secondstage, which is known as "color rendition" or "color halftoning". Herethe colors and image spaces should be reproduced on the printedpage--but both are found to be distorted, relative to those on thescreen, in peculiar and incomprehensible ways.

These latter artifacts are even more troublesome in the sense that theyare completely beyond control of even the most patient user. Priorskilled workers in this field have been unable to satisfactorily resolveeither problem.

This section of the present document undertakes to cast the operatingproblems of prior systems in terms of basic principles of color. Theresult will be a hint that whatever adequate solution may be found mustnecessarily result from a resort to first principles of color theory.The hint will be borne out in later sections explaining the presentinvention.

a. Dimensionality of color

Color is three dimensional. This tridimensionality is first traceablephysiologically to the origin of the color experience in at least threedifferent photosensitive pigments (or pigment-filter combinations) thatform the operative light-processing equipment of the retina.

Moving next to the physiology/physics boundary, arising from theoperation of those three sensors there apparently results acorresponding set of three spectral weighting functions--evidently partof the human viewing apparatus though perhaps partly in the brain ratherthan the retina. The capability of a human observer to make colordistinctions can be emulated by devices using these weighting functions,called "tristimulus" functions (International Commission onIllumination, 1931).

Proceeding on to psychophysical terms, the dimensionality of color isseen in Grassmann's First Law (1853): human optical apparatus is capableof exactly three kinds of color distinction. These can be expressed aschanges in dominant wavelength, luminance and purity.

Next at the purely psychological or perceptual level, we will inevitablyencounter again three variables. Quantitatively, however, not one butseveral competing coordinate systems or so-called "color spaces" havebeen introduced to describe the three-dimensional character of colorperception.

The root reasons for this proliferation of divergent perceptual modelsare at the heart of the present invention and will be discussed atlength. First, however, it should be appreciated that there is yet onemore level or environment, one more space, in which the tridimensionalcharacter of color must be manifested--machine space.

It is interesting to notice that in a sense we here come full circle,because the eye is a color machine; the pigment-based system that drivesit is as chemical, as electronic, and as mechanical as any artificialdevice. Now, however, we refer not to devices for distinguishing colorbut rather devices or machines for generating, producing, creating ormanufacturing color.

The color space used in such color devices in fact mimics or tracks thecolor space of the eye, in certain important ways. The three retinalpigments evidently absorb selectively in (very broadly speaking) theblue, green and red spectral regions, and these are the spectral bandsembodied in the tristimulus functions.

Evidently those spectral bands have some claim to special status as whatmight be called "natural" reference points for human color vision. Aswill be seen this fact sometimes has been a cause of confusion in designof equipment for color generation and control.

When we want to design devices that create and manipulate colorexperience, we aim to stimulate and control each retinal pigmentindependently. We would like to reach into the retina and excite justcertain sensors, and we know just what tools can be used to do so: blue,green and red light respectively.

These choices are also desirable from the standpoint ofcost-effectiveness. We must pay for each milliwatt of light that we useto create color sensation, or even to create any visual sensation, andwe do not wish to do so with light that falls between, or outside, thepeaks of spectral sensitivity in the retina.

Hence the choice of red, green and blue phosphors in video displays, andpigments of those same colors (or, for reasons to be discussed, theircomplements) in devices that produce color on paper and other media. Thepresent invention does not undercut these choices of machine colorants.

At some level of machine operation it is necessary to communicate inmachine language. At that level the machine needs a specification ofwhat colorant to drive, and so the machine language is necessarilycolorant language--for printing devices, pigment language. (In thisdocument, a machine "pigment" means a physical coloring substance.)

b. Fundamental color spaces for color manipulation, and criteria fortheir selection

A natural concomitant of these phosphor and pigment choices has been thehistorical use of a three-dimensional color space in which red, greenand blue are the defining dimensions R, G and B. For purposes ofcomparison only, FIG. 1 shows in an abstract form how such a space mightbe formulated.

For reasons that will shortly appear, color is seldom discussed, andalmost never manipulated by people, in such a space. Again, however, forthe lowest-level machine color space--analogous to the stream of onesand zeroes necessarily used at the lowest level in operation of adigital computer--the RGB-space choice is sensible.

Now it might be supposed, since R, G and B signals drive machinecolorants, and RGB stimuli drive the retina, that RGB space is an idealspace in which to manage all color transactions. In support of thisproposition can further be raised the fact that we not only work withRGB in operating our eyes but we also recognize those same colors.

That is, we consciously perceive them as such. Since it is theperceptual level that is of greatest concern for purposes of the presentinvention, the RGB space may seem perfectly qualified to serve for colormanipulation and navigation.

We shall digress to discuss why this is not so. Experience shows thatwhen humans need to navigate in color space their intuitions about thedirections that will take them to a desired result are totallyinadequate--if that color space is an RGB space. To begin with, thatstatement is true qualitatively:

Suppose we want some part of a color graphic to be "more reddish", or"less reddish", and we adjust a redness control to effectuate thatjudgment. If we are observant, we are often baffled to find that partsof the image now become more vividly or less vividly colored, and partsof the image become lighter or darker. Furthermore, the added ordiminished redness that was desired--and, we know, physicallyprovided--may or may not even be perceptible.

The above statement of inadequacy of our intuitions is even morestrikingly true quantitatively. Suppose that the person who wants somepart of a color graphic to be "more reddish" is a knowledgeable colorscientist who understands thoroughly what causes the baffling eventsjust described. That person now will realize what compound blendings ofcolor stimulus would result if merely the redness were turned up, andwill understand also what overall maneuvers must be made to drive to thedesired result.

As a general matter such a person will be able to make adjustments--of Rand G and B--that will move in the right direction in trispace. Eventhat person, however, will find it extremely difficult to gauge inadvance roughly how big the adjustments should be to closely approachthe desired result with just one or two sets of adjustments.

Therefore it is desirable to drive the RGB machine-language stage of acolor system with some other stage in which color can be manipulated ina more intuitive way. It is in recognition of this consideration, forexample, that color television sets are provided with color-adjustmentcontrols that are not labelled "red", "green" and "blue"--but ratherwith words intended to carry some intuitive connotations for guiding theuser more directly toward a desired result.

The stage of the system which is inserted to allow for adjustments mustproduce output signals that are then converted into RGB signals, by anarithmetic transformation. That manipulation or adjustment stage alsomay be driven by input signals received from a computer-screen controlsystem, or from a broadcast signal, or from a video-playback device--anyof which, in principle, may be in RGB.

Now we come to the question of what color space should be employedinside the adjustment or manipulation stage of the system--the so-called"color compensation" stage mentioned earlier. This space, sincenavigation is the only or principal reason for its existence, should beone which is navigable as intuitively as possible.

Essentially all modernly significant efforts to develop such aspace--including that of the present invention--lead to some derivationfrom the parameter set which FIG. 2 presents in a generalized form. Inthis space, color is characterized by the following three components orparameters.

(a) One of these relates to what has been termed "a mode of appearanceof the color"--see Judd, Color in Business, Science and Industry, SecondEdition, p. 45 (Wiley 1963)--and is often called "value".

In speaking of self-luminous objects it is also called "brightness"(ranging on a scale from invisible to dazzling); in reference to otherobjects it is "lightness" (on a scale from black to white).

The other two perceptual variables describe the chromaticness of theperception:

(b) hue--commonly used to describe the colors around a color wheel, and

(c) chroma, which is the saturation or vividness of a color.

This basic or fundamental set of parameters is often identified as the"Munsell HVC" color model.

As is well known, this parameter set is popular primarilybecause--besides potentially providing a full quantitative, analyticaldescription of the experience of color--it also corresponds toproperties of color that are readily grasped intuitively and that seemto be natural or even fundamental. The parameters correspond closely inintuitive significance to the three variations identified in Grassmann'sFirst Law.

As seen in FIG. 2, a familiar implementation of Munsell color spaceretains some grounding in retinally-referenced colorants R, G and B. Hueis seen as the angular element of a polar-coordinate system, on asix-unit cyclical scale from zero through five (or six superposed uponthe origin angle zero), and those three color reference points aregenerally identified as related to the points zero, two and four on thehue scale.

In this context the RGB points are no longer dimensions or parametersbut rather only numbers along a parameter scale; they are called"primary colors" or "primaries". As is known, the R, G and B on apractical scale need not be identically the color reference points thatearlier were suggested as "natural". Desired colors can be constructedfrom colorants that only roughly approximate those "natural" spectralsites--or indeed from other colorants that provide adequate chromaticgamut.

The value or lightness scale passes perpendicularly through the vertexor central origin of the hue plane drawn in FIG. 2. That plane ispositioned in the drawing to suggest that the origin of the value scalemay be taken as the center of the lightness-darkness range, with numbersL (light) as greatest available positive value and D (dark) the greatestavailable negative value.

The vividness or chroma scale is represented by perpendicular radial orhorizontal distance from the central lightness-darkness line LD. As willbe seen, this seemingly straightforward representation has led to someof the greatest problems in color-control efforts heretofore.

Of course any point in this tridimensional color space can berepresented with these three parameters. As a matter of chromaticreality, however, not all points in this space have distinct physicalmeaning.

Some constraints are imposed by theoretical availability of pure colorsin the spectral sense. In adapting this color space to generation ofcolors by use of fixed individual primaries, further constraints areimposed by availability of actual colorants.

Accordingly the ranges of permissible points are often said to beenclosed within various forms of color "solid". One such color solid isshown--again in very generalized form--in FIG. 3. Both the externalcontours and internal structure of that solid are characterized andillustrated differently in different color models.

Since the present invention proceeds from a way of thinking about colorspace that is fundamentally different from ways employed earlier,particularly as to color machines or devices, we shall continue slightlyfurther with our summary of portions of the conventional analysis.

FIG. 3 may be taken as representing very generally the colors availablefrom a large choice of colorants. The solid has rounded upper and lowersurfaces.

Those surfaces represent the boundary of the so-called "gamut" of thosecolorants--in other words, the extreme boundaries of the range of allavailable pigment choices, and combinations of those choices. All thecolors that are within those gamut boundaries can be formed from thoseavailable choices and combinations, and are said to be within the gamutof available colors of the system.

The limiting case of pure chromatic or spectral colors defines theextreme equatorial rim, or a vertical tangent along that rim--which inany vertical-section plane is rounded.

The top and bottom apices represent the light and dark extrema availablein the particular colorant system. These light and dark extrema, likeother points on the surface of the solid, correspond to the light anddark extremes of available pigments--here specifically the nonchromaticpigments.

The color solid of FIG. 3 has been drawn with a section removed. The twofaces 11a, 11b of the section represent the gamut of colors available,for the assumed large selection of colorants, in two different hueplanes. That is, each section face 11a, 11b respectively represents onlycolors that are formed by making a great variety of lightness andvividness shadings of one specific hue, exclusively.

FIG. 4 is a like generalized representation of colors available from aselection of many primaries of different hues, but just one primary foreach hue. The rounded surfaces are replaced by straight lines whichconnect the light and dark extrema, respectively, to the rim.

All these lines considered together form a pair of opposed cones. Therim now represents just one single point for each hue--corresponding tothe physical primary selected for that hue.

Thus the rim is now the sharp intersection of upper and lower cones.Further, as a practical example the boundary rim line at each point inFIG. 4 is defined by a color point that has been selected as within thecolor solid of FIG. 3: real-world colorants usable in machines usuallymust be selected to accommodate machine constraints on viscosity,physical and color stability, and cost. For the same reason the apicalpoints are chosen within the lightness range defined by the apices ofFIG. 3.

FIG. 4 thus represents one major step from the relative abstraction ofFIG. 3 toward practical machine systems. Implicit in FIG. 4, however,remains an assumption of an essentially infinitesimal spacing of aninfinite number of primaries about the rim. The next step toward apractical system is to replace these by some small number--such as threeto seven--of colorants spaced somewhat evenly about the rim.

Only colors within the boundary formed by a straight line between eachprimary can be formed from those colorants; hence the gamut of thesystem at its equator becomes a polygon. Above and below that polygonalequator, the gamut is defined by planes extending from the sides of thepolygon to the top and bottom apices; such planes form a gamut solid(not illustrated) composed of two opposed polygonal pyramids.

FIG. 5 shows four fine leaves 11R, 11PB, 11pg, 11Y sectioned from alarge-colorant-selection solid very generally like that of FIG. 3. Suchsections are called "hue pages".

Near top and bottom on each hue leaf or page 11R, 11PB, 11pg, 11Y thereis drawn a set of diagonal straight lines such as would be found from asingle-colorant-per-hue color solid very generally like that of FIG. 4.Superimposed for reference is a cylinder of constant vividness.

The hue pages here are merely for representative hues, but are far morerealistic than in FIGS. 3 and 4. They illustrate very clearly that theequatorial rim sweeps about neither a constant-lightness height noralone a constant-vividness radius--but rather varies strongly, as athree-dimensional contour, with hue.

Thus both blue-green 11BG and red 11R gamuts are available with maximumvividness that is positioned at midlightness values along the vertical"value" scale. Blue-green vividness is distinctly truncated, whereasavailable vividness for red is emphatically greater than for othercolors.

Purple-blue 11PB and yellow 11Y, on the other hand, both have verygenerally midrange vividness extrema; the purple-blue vividness comes toa peak at a very low point along the value scale--producing availablecolors often described as "deep". The yellow vividness, however, peaksvery high on the value scale, to offer colors sometimes called"brilliant".

From FIG. 5, and particularly by reference to only the straight lines oneach hue page showing the available gamut on that page for somepractical colorant of that hue, it is possible to visualize a colorsolid in which the straight lines in the four different hue pages areconnected together by triangular planes. At the outer edge, these planesform an irregular rim, not a regular equator as previously suggested.

That rim rather is a highly irregular one that pokes radially in and outto the different vividnesses of the several colorants, while riding upand down to the corresponding different lightness values at thosevividness points. The solid so described would represent the gamut ofcolors that could be formed by direct combination of the fourpractically usable primaries selected just inside the radially outermostpoint of each hue page in FIG. 5--under the constraint of using each ofthose primaries only directly as a primary.

As can be appreciated from visualizing such an irregular pyramidalsolid, with four (or more typically just three) colorants, very largeperipheral (i.e., vivid) regions would be cut off by the outer pyramidaledges--and so would be outside the solid. Those regions would representcolors excluded from the gamut, leaving distinctly limited treatments ofvivid colors situated between the colorant primaries.

Actually the gamut is not that severely constrained, even with onlythree colorants. Each pair of those colorants can be blended toconstruct a complementary color at a generally diametrical point of thesolid.

These complements can then be treated as if physically present, and thepolygonal equator thus puffed out (angularly) in the regions between theprimaries that are physically present. Accompanying that equatorialrestoration is a corresponding expansion of the pyramidal upper andlower surfaces.

Now when color is analyzed for the purpose of systematizing itsgeneration or manufacture--and especially in allowing users andautomatic-machine designers to adjust or control the resultingcolors--it has been natural to attempt to adapt these same three colordimensions to the analysis. Device users would like to be offeredcontrols or adjustments which they understand in intuitive terms: forexample, a knob labeled "brightness" or a computer-screen menu choice(for color to be printed on paper) marked "vividness".

To draw an example from an analogous (phosphor-based) field, however, itis a commonplace observation that twisting the brightness control on atelevision set is likely to change not only the brightness but thesaturation and even the hue as well. Chroma adjustments often areequally frustrating because the desired fine retouching of colorsaturation is often accompanied by gross changes in brightness--or,again, hue.

This example merely serves to couch the problem in familiar terms.Analogous difficulties are seen in all kinds of paper or so-called"hardcopy" color images: we all encounter marginal color renditioneverywhere in everyday life.

Behind the scenes, in many of such cases, were efforts to correct whatseemed to be just a small error in, for example, hue--but which effortsalmost inevitably resulted in unacceptable accompanying shifts in chromaor brightness.

Such results are a direct result of the unfavorable economics initerative efforts to bring the finished colors into a reasonableapproximation of what is desired. When iterative efforts fail (as isoften the case) to converge but rather seem to circulate endlesslyaround the desired accurate or natural appearance, terms such as"uneconomic" hardly suffice.

Two conclusions may be drawn about the present state of thecolor-compensation art: (1) color adjustments, identified by parametersthat are readily comprehended as intuitive, suffer from a lack of mutualindependence; (2) apart from that seemingly basic property undercontrol, color adjustments also fail to be reasonably well-behaved inperceptual color space.

Although our earlier discussion of RGB color space emphasizeddifficulties of independence of available adjustment parameters in RGBspace, we also mentioned the problem of quantitation of adjustment.Unfortunately, prior efforts to develop a formulation for intuitivemanagement of color have seized with excessive vigor upon this secondcriterion--quantitative regularity.

It is true that in discussing color as perceived, it is helpful toemploy a color space that is perceptually linear--in other words, aspace in which equal steps along any dimension correspond to incrementsof color perception that also appear substantially equal.

Adoption of that criterion as the major objective, however, has been tothe considerable detriment of the more fundamental criterion, parametricindependence. It is at this point, as will now be shown, that the priorart veers sharply away from satisfactory solutions to the problem ofproviding good adjustability.

This detour taken by the prior art is not a fault inherent in thefundamental HVC color space of FIGS. 2 through 5. Rather it arises inunfortunate choices for specific definitions of theparameters--particularly chroma C.

True independence (or in mathematical terms "orthogonality") ofparameters may be unnecessary, but at least very low mutual sensitivityor crosstalk is highly desirable. Similarly, precise perceptuallinearity may be unnecessary, but it is sensible to pursue at least afair degree of consistency in response to like adjustments of chroma,for example, in different portions of a hue plane. The same is true ofuniformity in response to like adjustments of brightness in the presenceof various chroma numbers; and so on.

In response to this line of thinking it might be objected that a cleardesign goal for the most modern equipment should be to substantiallyeliminate the real need for adjustment, and simply drive the colordevices to a color presentation that is both "correct" or "accurate" and"natural". For two reasons, the requirement for independent andwell-behaved parameters in an adjacent color space cannot be so easilydismissed.

First, consumers will continue to want fine adjustments for use as amatter of taste or preference. Second, in modern apparatus intended toproduce correct or natural color the same problems of parametricindependence and regularity resurface before the color device reachesthe consumer: here it is the apparatus designers who struggle with thesame problems.

The reasons for the importance of independent parameters are the same insupposedly automatic color-control systems as in an earlier generationof systems nominally dependent upon operator adjustments. The colorantsused to produce color--pen-discharged ink dots, for instance--simply donot come with inherent, independent adjustments for chroma, brightness,or hue.

None of these physical substances is an ideal Munsell color machine.Neither are the devices--e.g., pens--used to actuate the colorants.

This momentary reversion to thinking about machine space and colorantlanguage does invoke a third conclusion: (3) the so-called perceptualprimaries and variables employed for color adjustment fail to correspondwell to "device primaries" and "device variables".

Here is a summary of the conclusions reached so far. Industrial colorscience has failed to develop a model of color space that is bothparametrically independent and perceptually uniform, and even moreemphatically has failed to develop a model that is also reasonablycompatible with device parameters.

The prior art has not reached a main objective: an ability to take theinput desired-color information into such a space. Therefore it is notgenerally possible for perceptually meaningful and independentadjustments, compensations and rendering decisions to be made easily andstraightforwardly--in particular, without need for iteration.

The prior art has also fallen short of another main objective: anability to move on into machine space with minimal distortion of theperceptual adjustments, compensations and decisions.

After some further introduction, two prominently used color models willshortly be described; as will be seen they fall short of all threeobjectives--independence, well-behaved navigation about color space, andcorrespondence to device parameters.

c. Operation of color-creating devices

Typical color output devices use a combination of--for example--red,green, blue, cyan, magenta, yellow and black colorants to generatecolor. These colorants conventionally are abbreviated R, G, B, C, M, Yand K respectively; or in a usual condensed notation "RGBCMYK". Thesesystems are only capable of printing these distinct colors, limited innumber, at each addressable location.

In this document these distinct colors will be called the systemcolorants. They include device primaries (i.e., chromatic colors RGBCMYthat have hue) plus black K.

Typically the system colorants also include white ("W")--commonly forexample the white of a sheet medium such as paper. In some cases whiteis instead constructed by blending chromatic colors--but when suchblends are used in trying to produce white on an already-white sheet ofpaper or the like, the result is to waste pigment. Analogously,overprinting two or more pigments to approximate gray always wastespigment and also usually produces a poor gray (i.e., one that is impure,in the sense that it includes a chromatic component).

Usually the number of actual system colorants--that is, thoserepresented on a one-to-one basis by physical pigment substances--issmall. In particular, instead of all eight colorants listed above, asmentioned in the preceding section it is common to form or constructsome (e.g., red, green and blue, RGB) as combinations of others (thecomplements cyan, magenta and yellow, CMY).

Nevertheless these constructed (as distinguished from actual) colorantsRGB usually are treated as device primaries available in theircombinable form. This latter part (combinability) of the assumptionresults in very helpful analytical simplifications to the process ofproducing other colors generally--i.e., other than the full set ofassumed system colorants RGB-CMY-KW.

In particular, in a system that has the six chromatic colorants CMY-RGB,plus black and white, it can be shown that in order to generate anycolor (within the saturation envelope of these colorants) using thedevice, it is necessary to apply only two colorants plus black andwhite. As will shortly be seen this technique for operating a CMYKdevice is important and valuable--but for a reasonably completehue/saturation gamut does rest upon the assumption that the constructedcolorants RGB do stand in some reasonable semblance of complementarityto the actual colorants CMY.

In order to create colors other than the actual system colorants CMYK,as is well known, the latter are positioned on the medium (e.g., white)in close adjacence. The viewer integrates perceptually the spectralbands physically emanating from the actual colorants.

The viewer thus perceives some color not present as a single pigment,and perhaps perceives a desired color or something near it. Of course,close inspection as under a magnifier reveals that that desired blend isnot represented as an individual colorant.

An important special case of this is halftoning, in which dots ofdifferent colorants are distributed over some area or region of themedium. Various degrees of freedom are available in such systems,depending upon the type of color device in use: dot size, for example,can be made variable.

In printing machines driven directly by digital computers, generallymore straightforward and rapid operation results from controlling onlypresence or absence of dots, but the dots and their spacing can be madequite small to yield reasonable overall resolution. With such machines,often halftone technique is called "digital halftoning" and the dots arecalled "pixels"--from the familiar convention of video display.

Many digital halftoning methods are extensions of the gray-scalehalftoning case, in which gray information is generated by combinationsof black and white pixels. These methods, when extended to the colorcase, typically assume that the colorants obey a subtractive color law.

It is for this reason that--as mentioned above--all six chromatic deviceprimaries RGB-CMY are treated as available in combinable form eventhough actually only three CMY (as well as nonchromatic K) arephysically present. When the printer or other device fails to obey thesubtractive color law, however, color errors result because it generatesdevice primaries R'G'B' which are treated as if they were complementsRGB to the actual pigments CMY, but are not those complements.

A better way to control the resulting color is to treat such a CMYKdevice as having six chromatic device primaries, and to construct threeR'G'B' of those as crosscombinations of the three actually present, asbefore--but to drop the assumption that the constructed ones R'G'B' orpseudoRGB are accurately complementary red, green and blue RGB. Thisreleases the need to depend on the subtractive color law, forestablishment of primaries.

Color combinations now can be calculated using actual properties of theconstructed primaries and indeed of all the primaries. Such asystem--with six known chromatic colorants corresponding at leastroughly to CMY and pseudoRGB or R'G'B', plus black and white--retainsthe capability to generate any color (within the available saturationenvelope) using only two of the colorants CMY-R'G'B' plus black andwhite, taking into account the known departures of R'G'B' from thecomplements RGB.

This capability in turn enables generation of any such color using justthe four actual pigments CMYK and the white background. In the remainderof this document we shall drop the notation R'G'B' and substitute thesimpler RGB, with the understanding that typically one or more of theseis a constructed primary.

Some known machines, particularly some using CMYK devices, arecontrolled by isolating black information K for separate processing inthe color-compensation stage. Those systems then retain the separateblack information channel in the halftoning or rendition-driving stage.

d. The HSV color space

FIG. 6 illustrates, for one traditional color model known as "HSV", theway in which perceptual variables H, S and V are found from a givendefinition of a desired color rendition. Those perceptual variables arethen used to control device variables (not shown).

Discussion of the HSV system is appropriate because that system could beused to control a computer-driven CRT monitor in preparing a colorgraphic--which can then be printed on paper by a device also driven bythe same computer.

The HSV color model corresponds to a color solid that is modified fromthose of FIGS. 3 through 5--which correspond more closely to theclassical Munsell HVC model. In HSV the color solid is just a singlepyramidal cone, rather than two opposed cones.

HSV is intended to model closely the intuitive concepts of tint, shadeand tone used by an artist working manually in paints. While it mayaccomplish this, it departs considerably from relationships in classicalHVC; the departures will be discussed in detail in the followingparagraphs.

In the FIG. 6 diagram, the full available colorant range or full-scalecolor range is identified as the constant Full at the top of the graph.The heights of the three bars marked "Rin", "Gin" and "Bin" representrespectively an example of the amounts or sizes of red, green and blueinput information--that is to say, an exemplary color that is defined as"desired".

Of course in any given real situation any one of the three inputs couldbe the largest, any could be the smallest, and any could be theintermediate or middle color quantity--so the identifications of thethree bars as Rin, Gin and Bin also are only an example. The relativeheights of these three bars also are only an example.

Generalized quantities--that is, the desired red, green and blue amountsin the general case--will here be denoted by the same notations initalic type Rin, Gin and Bin.

In any situation, however, there must in fact be some largest, somesmallest and some middle color amount: to facilitate general treatment,therefore, the three bars are labelled "Max", "Mid" and "Min"respectively These same notations in italics--Max, Mid and Min--will beused to designate the relative bar heights in general, which is to saythe three color quantities without regard to which is blue, red orgreen.

For simplicity we define or normalize Full≡1, so that all the numbersRin, Gin, Bin, Max, Mid and Min are fractions. In typical machineoperations Full is assigned some conventional numeric value such as 255,chosen for adequate dynamic range, and the other values are all countstoo. Relative representation of all the numbers in this document asintegers rather than fractions is to be considered equivalent to thefractional notation.

(These same understandings apply to FIGS. 9 and 11 too.)

Now we turn to the matter of conversion from RGB color space into HSVspace.

In the HSV model as in other generally used polar models it is common tostart by determining which of the RGB primaries is the largest, smallestand middle quantity, respectively, and assign values for Max, Mid andMin. Next, conversions from the input information to perceptualvariables include three determinations.

One of these is a direct measurement of the variable "value" or V. Thisvariable is set equal to the largest input number, V≡Max.

A second computation is addressed to "saturation" or S. It is set equalto the difference between Max and Min, but normalized by dividing intothat difference the value Max:

    S≡(Max-Min)/Max, or 1-Min/Max.

A third computation determines the hue, according to a somewhatcomplicated formula: H≡C+Fh, where

    C=0 if Rin≧Gin≧Bin

    C=1 if Gin≧Rin≧Bin

    C=2 if Gin≧Bin≧Rin

    C=3 if Bin≧Gin≧Rin

    C=4 if Bin≧Rin≧Gin

    C=5 if Rin≧Bin≧Gin

    F=(Mid-Min )/(Max-Min ) if C is even

    F=(Max-Mid )/(Max-Min ) if C is odd.

This treatment--as well as the use of the hue variable--underlies allprevailing color models, including that used in the present invention.

This quantitation scheme is a specific implementation of theperceptually uniform Munsell HVC color space which we have illustratedand discussed at length, but now applying specific quantitative andconceptual definitions to the generalized Munsell concepts.

One major weakness of the HSV-system is that V is set equal to thelargest primary quantity present, regardless of which primary it is--andregardless of the amounts of the others that may be also present.Machine adjustments of brightness or value, conversely, are theneffectuated by setting the largest primary color level equal to theuser's desired overall value, or brightness, or intensity.

This is quite inadequate, because it fails to take into account eitherthe spectral sensitivity function of the eye or the amounts of othercolors that are present. Perceptually such other colors add to theapparent brightness, in complicated ways that relate to--among otherthings--the visual sensitivity of the eye in the corresponding differentspectral regions.

One way to appreciate the problem of this misdefinition of value is toreview FIG. 5. It suggests that some true or intuitive perception oflightness for saturated yellow may be in the neighborhood of 0.87, butfor saturated purple-blue and red respectively may be only 0.42 and0.38--less than half that found for yellow.

Another major inadequacy of the HSV model is the normalization ofsaturation S to the largest primary present Max. Conceptually a reasonedargument can be made for such a relationship, but it results in aninverse proportionality, rather than independence, between twoperceptual variables S and V.

FIG. 7 shows parametric relationships on a representative hue page111--such as any of the leaves of FIG. 5--in the HSV color model. Thehue page is viewed perpendicularly.

The top diagonal line is defined as a line of unity value V. The bottomdiagonal line is defined as a line of unity saturation S.

A great number of different examples could be presented to illustratecounterintuitive consequences of using such a system. Following are justthree.

Suppose that a device user assigns a saturated red color to some theregions in a particular graphic and a saturated yellow to others--andthen instructs the device to make all the regions equally light. TheHSV-controlled device, however, will interpret this as a command to makeall the regions of equal value V as defined.

It will make corresponding adjustments and report the missionaccomplished. The puzzled user, however, will see clearly (andconsistently with FIG. 6) that the yellow regions are twice as light asthe red regions.

Next suppose that a user wishes to move 112 from a relatively lightcolor of medium vividness to a relatively darker color of the samevividness and hue. The user is quite satisfied with the startingvividness: the color is not too gray, not to chromatic--just right inchroma--but just a little too light.

Thus the user, in effect, wishes to move vertically 112 within a huepage such as that of FIG. 7. Curiously, however, while continuing tocall for progressively lower lightness (or greater darkness) the userwill find 113 that the vividness is decreasing along with the lightness.

If progress on the FIG. 7 hue page could somehow be followed, the userwould be surprised to find that the HSV control system, though receivingan instruction to change value only, is pursuing a diagonal route suchas the path marked in FIG. 7. Not always available, however, is eventhis kind of map-like assurance that the user is not being deceived bythe user's own senses.

The operator simply sees that the carefully adjusted, satisfactorilyvivid starting color is becoming not simply darker, as desired, but alsobecoming, as the user might put it, "ruined". In more analyticalcolor-science language, the color is becoming grayer or less vivid: thecombination of the two effects is a color effect often called "dirtier".

At this point the user usually concludes that the control system is oneof those familiar examples of a modern device to which the user becomesa servant. The user believes that the system can be made rational if theuser will only develop a mental calibration--an attunement by the userto the degree of dirtiness that can be expected in darkening a color.

To make matters worse, however, just when the user may think acollaborative person/machine control stratagem has been found, thesystem is likely to defeat even those newly sophisticated expectations.Here the contortion is more subtle, but thereby seems only all theharder to grasp:

If the user happens to be operating in a more-saturated region than theone in which the user performed the mental self-calibration, the systemmakes the rate of dirtying per unit darkening rate higher (a steeperslope for the path, if it could be seen). If the user happens to be in aless-saturated region, on the other hand, the system makes the dirtyingrate with darkening lower (a shallower slope).

A third example: a user has found a color that is satisfying in allrespects except that it is not quite vivid enough.

The user wishes to raise the vividness without changing the brightness.That means, in classical Munsell HVC terms, a positive radial movement:a horizontal movement 114 away from the lightness axis.

The user will find here that the color becomes not only more vivid butalso darker--or, in other words, deeper. FIG. 8 shows the path 115followed.

Deep colors can be very appealing, but that is not what this particularuser wants. The user may attempt to correct by increasing 116 lightnesswith the "lightness" control, but in the previous example the controlsystem will respond with increased vividness too.

The user started out to raise the vividness, but had already moved it toa desired level, so now the control system is forcing the user toovershoot the desired vividness. The user now must lower the vividnessto compensate for that.

Again, if able to see the map, the user would begin to doubt therationality of the navigation system. The user would see that outward(toward-vividness) movement obtained with the "saturation" control aloneis accompanied by downward (toward-darkness) movement.

Given the user's experience with the first iteration, the user feelsthat thereby a degree of intuition has been achieved as to operation ofthe control system--but now the the user makes another disappointingdiscovery:

The adjustments required to obtain a desired incremental change ofvividness will produce an accompanying change in lightness too--but at adifferent rate than before. In other words, the ratio of lightnessincrement to vividness increment is different, so that not only is thedesired color not obtained but also the user's feeling of makingprogress in understanding how to use the system is defeated.

e. The HSL/HSI color model

FIGS. 8 and 9 represent another popular color-control protocol known byvarious acronyms such as "HSI", "HSL" and "HLS". Here the parameters arehue, saturation, and intensity or lightness--once again corresponding ina very general way to Grassmann's First Law and to the generalizedthree-dimensional color spaces of FIGS. 2 through 5.

The definitions of these control axes, however, differ somewhat fromthose in the HSV model already analyzed. This can be shown by comparingthe expressions given above for converting RGB coordinates into HSLsaturation S and value V with the analogous expressions for obtainingHSI/HSL saturation S and lightness L or intensity I. (To simplifymatters we will use only the variable L, which is more appropriate forsystems that print on paper as distinguished from self-luminous systemssuch as CRT displays.)

While hue is the same, the other two variables are determined from theseformulae: ##EQU1## Another way to write the expressions for saturation Sis: ##EQU2##

At the outset it can be appreciated that the definition of lightness asan average of two primary quantities, namely the strongest and weakest,is intended to--and does--ameliorate the unnatural selection (in the HSVsystem) of lightness as equal to the single strongest primary.

The dual definitions of the saturation S reflect the fact that HLScreates an opposed-cone color space, more similar in this regard toclassical HVC than the HSV space. In this respect the HLS system may beseen as more advantageous.

Nevertheless the saturation S here remains inversely proportional to alightness or darkness parameter L, 1-L (depending upon whether the colorof interest is above or below the midlightness plane defined by L≡1/2).This inverse proportionality gives rise to interdependencies andconfusions of the same sort as discussed above for HSV.

It will shortly be shown, moreover, that the interaction between thisinterdependency and the dual definitions of saturation S introduces anew element of operational mystification. This far surpasses thedisorientations encountered in HSV space.

As noted in FIG. 9, the upper and lower straight-line borders of the HSLhue page--connecting the upper and lower apices on the value axis withthe defined primary--are here treated as a single locus of constant,maximum saturation.

In other words, each point along each of these two lines, as well as theequatorial apex, represents the greatest vividness that can be obtainedfor the particular lightness value at that height on the outer surfaceof the color solid. This interpretation alone, without consideringnavigation within the interior of the solid, does violence to intuitivefeelings about color.

To see that this is so, consider a color on the outer surface very nearthe upper apex of the solid--that is, along the top diagonal line, butnear the top-left corner. This color in truth appears to have virtuallyno vividness at all; it is nearly pure gray, because its horizontal(radial) distance from the lightness axis is extremely small.

Furthermore on the gray scale it is nearly white, because its verticaldistance from the "light" pole is extremely small. Nevertheless in theHVC system this exceedingly pale color lies along a constant-saturationline which passes through the pure-primary colorant point at theequatorial apex and so is is said to have the same--namely,maximum--saturation (still regarded as a measure of vividness) as thatpure-primary colorant.

Also assigned the same saturation is a color on the outer surface verynear the lower apex of the solid--i.e., along the bottom diagonal line,near the bottom-left corner. This color too appears to have negligiblevividness: it is an extremely dusky or dirty color, nearly pure gray andnearly black, but lies along the same constant-saturation line as theextremely pale color point (and the pure-primary colorant) consideredpreviously.

If two colors are compared that are both along the two diagonal outerlines, in general the system's navigational equipment reports adifference in lightness. It persists in the interpretation, however,that no difference in saturation (vividness?) can be detected.

Small wonder that a user relying upon such a system is confused! This,however, is not the end of the story.

When the user takes controls in hand and moves off the relatively safeboundary of the solid into the interior, the maneuvering rules aregenerally analogous to trying to drive across a large, open, seeminglystructureless which requires indirect routes. To simply move to a planeof greater lightness, the user shifts the "lightness" control--butinstead of maintaining 212 a color of intuitively or perceptuallyunchanged vividness (FIG. 10), the perceived vividness first boundsrightward 215 to a maximum and then--with no change in direction ofoperation of the "lightness" control--reverses field and dives backleftward 217, 217', toward no vividness.

An undesirable result arises also in attempting to simply raise or lowerthe vividness. In complying with such a command the HVC autopilot willnecessarily set off on a horizontal course 213, and reasonable responseto adjustment will be enjoyed when the user is operating in, say forexample, the midlightness region (FIG. 11).

Response would be slow, however, near the apices, the very-light andvery-dark regions--and after cranking on the control for a long while213' the user may be dismayed to find that a lot of time has beenwasted: the end of the adjustment range will have been reached withoutreaching any appreciable perceived vividness.

Perhaps the machine designer will notice these effects and selectinstead a lightness region some two-thirds of the way toward top orbottom apices, and assign the full adjustment range to the correspondinglength of the constant-lightness line at that height. This will be animprovement--but still by definition of the system cannot meaningfullyimprove performance very near the apices.

Such a redefinition of the control scale would be a typicalaccommodation or so-called "engineering tradeoff", but now results inunsatisfactory operation 213 near the midlightness point--in the rangemost often used. Now the control produces relatively large horizontal(radial) steps for relatively small adjustments, trying to equalize theincremental progress at the middle of the color solid with the analogousincremental progress at top and bottom of the color solid, in terms ofsaturation as defined.

Unfortunately now the high effective leverage of the control knob in themidlightness range will produce relatively large changes 213 invividness as perceived, for relatively small adjustments. The machine,in short, now oversteers in perceptual vividness, making the vividnessreact too abruptly to small steering corrections.

The system condenses all of the user's potentially desired range ofvividness numbers into a very small part of the available range ofadjustment--and wastes a large fraction of that adjustment range. (Atthis juncture the skilled designer may join the user in dismay: it isnot only hard to control the system but hard to produce a satisfactorydesign.)

Such operation may be more than merely annoying if the adjustment isattached to a digital control with a relatively limited dynamicrange--such as the popular numbers zero through 255. That would be areasonable expectation, since the control system is touted asperceptually uniform and in a truly uniform system 2⁸ bits shouldsuffice.

In this case the entire candidate range of perceptual vividness could beforced into a narrow numerical interval. With that much granularity itwould be a coincidence for the user to find an available vividness thatis considered suitable.

Of course the system designer has a number of available options, such asgearing the adjustment sensitivity to lightness or providing "fine" and"coarse" adjustments, or allowing the user to set the adjustment rangeabout a desired point. To begin with, the skilled designer in generalmay have little-better view of the FIG. 7, 8, 10 and 11 road maps thanthe user, and so may be unable to systematize the observations enough tosee what the problem is.

Furthermore the designer who somehow is able to see those strangedetours taking place within the color solid may not be able to perceivehow to prevent them.

f. Conventional operation of color-rendition drivers

As already mentioned in section c, computer-driven color devices forprinting color images on sheet media generally produce colors as blendsof just a few physically present colorants--and do so by takingadvantage of the observer's ability to perceptually blend physicallyadjacent color dots.

In a sense this technique could be said to exploit a weakness ratherthan an ability of the observer, who is simply unable to resolve closelyadjacent fine details and instead substitutes a perception as to theircomposite meaning. In any event the adjacency-blend technique forconstructing a color pattern, diagram, picture or other graphic is wellestablished.

Generally a separate computational stage--sometimes even embodied in aseparate apparatus--is employed to determine the assignment of differentcolorants to the various available dot positions in a color-halftonegraphic. This colorant-to-dot-position assignment stage is sometimescalled "digital halftoning" or "rendition" of the desired color.

Since this rendition driver must make decisions about actual machinecolorants, naturally it operates in machine-colorant space. Commonlytherefore the earlier color-compensation or adjustment stage includes atits output a conversion step in which its perceptual-space decisions aretranslated (often translated back) to machine language--i.e., colorantspace such as RGB or CMYK--for use in the rendition.

After such a system has done its work, it is natural for a user tocompare the printed results with the desired-color input on the CRTscreen. Such comparison generally reveals that the rendition driver hasselected, for individual dot positions, colors that do not appear at allin the on-screen definition of desired color.

It might be thought that such distortions would affect only a fewisolated dots, virtually invisible in large fields of color. Even in theinteriors of large fields, however, that is not reliably so. At abruptcolor-field boundaries and particularly in relatively small regions ofdistinctive color, especially serious problems can arise.

In those contexts, conventional digital-halftoning schemes allowaccumulated errors to propagate as quite visible and even conspicuoussprinklings of chromatically anomalous dots. Critical customers findsuch renditions unacceptable.

The system workings that produce these questionable results will now bedescribed.

Conventional digital color halftoning has evolved from a techniquedeveloped in monochrome by Floyd and Steinberg, "An Adaptive Algorithmfor Spatial Gray Scale", Intl. Symp. Dig. Tech. Papers at 36 (SID 1975).The original technique, for use in devices using only twocolorants--black and white-- attempts to make statistical decisionsabout pixel-printing locations in such a way as to yield a smoothrendering of desired gray-scale information.

At each printer pixel location (x,y), the decision whether or not toprint a black dot is made by comparing the total desired grayinformation Dk--in terms of white W≡0, and black K≡1--to a fifty-percentthreshold. The subscript "k" identifies the processing as relating tograyness or in other words a quantity of black colorant.

If the quantity of the total desired monochrome level Dk is greater thanthat fifty-percent threshold, Dk>1/2, then the pixel is printed black.Otherwise it is printed white--which ordinarily, with a white medium,simply means left unprinted.

In either case, in general an error (Ek) is generated which representsgray information that is not yet taken into account in terms of whatactually appears on the printed medium. Subsequent pixels must accountfor this residual Ek.

When a total desired grayness level Dk is less than fifty percent,Dk<1/2, and a dot is therefore not printed, the error Ek from that pixelposition is equal to the entire amount of the unrelieved quantityDk--that is, the total desired quantity Dk minus the actual quantity 0,for a deficiency of Ek=Dk-0=+Dk. When the total desired grayness Dkexceeds fifty percent Dk>1/2 and a dot is printed, the error from thatposition equals the total desired quantity Dk minus the printed quantity1, which comes to an overshoot of Ek=Dk-1, a negative number.

The error information Ek, whether positive or negative, is weighted andaccumulated in future pixel locations--typically several differentnearby locations--for use when those pixel decisions are made. FIG. 12illustrates a conventional pattern for distribution of error from anactive pixel (x,y), in other words the pixel for which a print decisionis being made.

As can be seen, this diffusion pattern moves various fractions of theerror from the active pixel into one not-yet-reached pixel in the samerow--in other words, the next pixel in line for decision--and into threepixels in the following row. Errors propagated to unused pixel positions(past the edge of the frame, for instance) simply are discarded.

More specifically, the distribution typically assigns to the adjacentpixel (x+1,y) in the same row 7/16 of the error. To the centrallyadjacent pixel (x,y+1) in the following row is assigned 5/16 of theerror, and to the two pixels (x-1,y+1) and (x+1,y+1) adjoining thatpixel 1/16 and 3/16 of the error respectively. (Various other allocationpatterns have been proposed, and some have been used, in attempts toobtain visually more satisfying results.)

Later the digital-halftoning system receives or takes up each subsequentpixel for processing of the desired grayness at its location. Beforemaking the threshold decision for that subsequent, then-current pixel,the previously accumulated grayness error Ek is added to the desiredgrayness K at the then-current pixel.

The sum represents the "total" desired grayness level Dk used in thealgorithm discussed in the second preceding paragraph. In that "thencurrent" pixel, grayness error Ek in general will have been accumulatedfrom several different nearby prior pixels.

These same procedures are described below in terms of formulae:

    Dk(x,y)=K(x,y)+Pk(x,y)

    Ak(x,y)=Round(Dk[x,y])

    Ek(x,y)=Ak(x,y)-Dk(x,y)

    Pk(x+1,y)=Ek(x,y)·7/16+P'k(x+1,y)

    Pk(x+1,y+1)=Ek(x,y)·3/16+P'k(x+1,y+1)

    Pk(x,y+1)=Ek(x,y)·5/16+P'k(x,y+1)

    Pk(x-1,y+1)=Ek(x,y)·1/16+P'k(x-1,y+1),

where

K≡desired grayness level, amount of black pigment

D≡decision to print pigment (computational); or "total" desired colorantquantity

E≡error propagated from the active pixel

A≡actual decision to print pigment

P≡total previous error

P'≡partial accumulation of previous error

x≡column number of the active pixel

y≡row number of the active pixel.

For reasons that will become clear, the decision and error variables D,E, A, P and P' as well as the position coordinates x and y are heredefined in general terms for any pigment.

The process continues until all pixel decisions have been made.Statistically all the desired grayness information elements K then havebeen used to provide the best rendering of the image.

As seen in FIG. 12, the error E generated in each pixel is typicallyspread out over several adjacent pixels, and a contribution from thaterror often can be regarded as redistributed or respread from those intofurther adjacent pixels--and yet further ones, and so on. This behaviorof the error is analogized to diffusion of a fluid; hence the term"error diffusion".

To effectuate this plan, an error-accumulation buffer or memory isestablished for each pixel location x,y as the progressive renditionprocess approaches that pixel. Errors allocated to that pixel fromothers previously processed are simply added into the correspondingbuffer.

In color applications, the Floyd-Steinberg method is applied to each ofthe components or primaries of the RGB or CMYK machine spaceindependently. That is, the pixel decisions for each device-primarycolor are independent.

Precisely the same formulae shown above for black are used for each ofthe machine colorants, except that for each chromatic primary of coursethe subscript "k" identifying black pigment is replaced by a suitabledesignation of that primary. Thus e.g., in the case of red,representative lines of the above formulae may read (F≡desired inputfraction):

    Dr(x,y)=Fr(x,y)+Pr(x,y)

    Er(x,y)=Ar(x,y)-Dr(x,y)

    Pr(x,y+1)=Er(x,y)·5/16+P'r(x,y+1).

For color machines that can print black K independently, an effort ismade to extract black information from the RGB or CMY pixels, andisolate that information to drive the black-printing device. Thisobjective is salutary, since color-black is in principle produced farmore efficiently and accurately by black ink than by combinations ofothers.

In general, however, such systems are able to extract only a rather poorapproximation to the desired black information, thereby introducinganother source of dissatisfaction with final printed colors.

To effectuate this plan in a color regime, the procedure establishes notjust one buffer but three or four--in any event, one buffer or memorylocation for each machine pigment in use--for each pixel beingapproached. Error contributions can now be separately added (takingaccount of their algebraic sign of course) for each primary colorant RGBor CMYK.

The procedure leads to three or four actual print decisions Ar, As andAb--or Ac, Am, Ay and Ak as the case may be--one for each colorant. Inevery way the decision for each pigment proceeds independently, toeither print one or more color dots (or white W--i.e., no dot) in eachpixel position.

In event the system decides to print more than one colorant in a singlepixel, that is exactly what occurs: the pigments mix and the resultingcolor is formed by the combined influences of the colorants. Assuggested already, it is often assumed that they will operate in linearsuperposition to produce the results predicted by a subtractive colorlaw.

As indicated at the outset, the rendition system just described allowsdots of all colors to propagate in areas where the desired color is ashaded device primary--which is to say, a combination of a purechromatic colorant with gray. As a particularly flagrant special case ofsuch situations, the machine output frequently contains colorinformation where the input color is only gray information.

These effects are readily seen in some flesh tones of scanned images, ingray-scale images, and most interestingly even in large solid fields ofshaded color--for instance, those used as backgrounds in businessgraphics.

Another manifestation appears at relatively abrupt colortransitions--sharp divisions between regions of distinctly differentdesired color. Often the colorants of one region diffuse into the other,blurring the demarcation.

Such performance results in color effects often perceived asincongruous. Lemons, for example, that are tinted with green dots, andlawns sprinkled with pixels of blue, call particular attention to theinability of the rendition system to track basic decisions laid downfirmly at the earlier color-compensation stage.

It should be emphasized that a rendition driver produces such effectswhile functioning correctly as designed. That is to say, as long asoperation of the halftoning driver is evaluated only in, say, RGB space,that operation may be found flawless: the colors just described as"incongruous" are perfectly valid representations of the RGB inputcolors to the driver.

Ironically the very characteristic that would be particularly prized inoperation of a perceptual color space employed for color-compensation or-adjustment purposes--namely, independence of parameters--is here seento be associated with major problems in operation of a machine spaceemployed for color-rendition or -halftoning purposes.

g. Summary

Prior color generation systems suffer from two distinct failings--firstat the compensation stage and then later at the rendition stage.

The first places difficult hurdles in the path of an operator or systemdesigner attempting to obtain color effects that are natural oraccurate--or simply preferred. The apparatus interprets perceptuallystraightforward instructions in counterintuitive baffling ways, whichrequire the user to struggle through multiple iterations in setting upthe target color effects (typically displayed on a CRT).

The rendition-stage failings defeat expectations of the user who haspatiently surmounted those operating hurdles at the compensation stageand has succeeded in creating a satisfactory color scheme. The user thenanticipates a printed output color rendition closely tracking thesatisfactory scheme, but finds instead a rendition containing blurredimage-element edges, bleeding colors, and perceptually irrelevantpigments even within broad fields.

The literature of the prior art in this field has failed to identifyeither of these problems in terms of basic color principles orotherwise. The prior art fails to find underlying relationships betweenthe two problems, and fails to resolve either one.

SUMMARY OF THE DISCLOSURE

In the course of making and refining the present invention, certaininsights have been gained. They explain fully the mystifying behavior ofthe prior color models and halftoning systems discussed above.

Those analyses will be presented in later sections of thisdocument--together with description of the current invention in a morenarrative or tutorial manner. Those later sections will permit a fullerappreciation of how the stated advantages flow from the character of theinvention.

In this section the invention will be introduced only in somewhat formalways, and its advantages simply will be stated.

The present invention has several different facets or aspects. Forfullest enjoyment of the benefits of the invention, all of those aspectsor facets of the invention are preferably practiced together.

As will be seen, however, significant advances over the prior art can beachieved by practicing certain of the aspects without others. For thisreason the several facets of the invention will now be introducedseparately.

In a first group of such aspects to be presented here, the invention isapparatus.

Now, within that group, in its first aspect the invention apparatus isfor use with a visible medium. The apparatus is also to be used withdesired-color information from a color-image source.

The apparatus comprises a device for causing the medium to appearcolored. It also comprises a programmed information processor forreceiving the desired-color information, generating device-controlsignals for the device and (in the course of generating them) producinga certain complex effect.

That effect includes at least these components:

A. resolving that information into hue, Fraction-Colorant and black orFraction-Black information;

B. performing color-compensation operations upon the so-resolvedinformation to generate the control signals for the device; and

C. expressing the control signals in a form applicable to control thedevice.

The meaning of the term "Fraction-Colorant" will be defined analyticallyin a later passage. For the present it will suffice to say that thisparameter is very easy to grasp intuitively--simply the component of theentire color that is made using chromatic colorant, as distinguishedfrom nonchromatic colorants such as black, white or gray.

In addition the apparatus also comprises some means for receiving thecontrol signals, in that device-control-applicable form, and applyingthem to control the device. As a verbal shorthand to retain generalityof reference, these means will be called the "device-control means".

The foregoing may constitute a definition or description of the firstaspect of the invention in its broadest or most general form. Even inthis broad form, however, this aspect of the invention is capable ofresolving most of the prior-art problems discussed earlier.

In particular by producing the effect of resolving the desired-colorinformation into hue, Fraction-Colorant and black information theapparatus produces the effect of embodying the desired-color informationin a form which is amenable to manipulation in a perceptually correlatedway. That is true for two reasons:

(1) true physical meanings of the parameters Fraction-Colorant andFraction-Black--as will be seen are intuitively grasped much morereadily than the true physical meanings of the artificially defined"saturation" parameters and "value" or "lightness" parameters of theprior systems discussed earlier; and

(2) the three parameters of the set are much more nearly independentthan the parameters of the prior-art color spaces previously developedfor apparatus that causes media to appear colored.

These characteristics make manipulations of color more tractable for twodifferent kinds of color-space users. Those beneficiaries are (1)end-users of equipment which has controls that are manual, and (2)color-system designers who wish to provide built-in color-compensationstages that are automatic.

Another advantage of the first facet of the invention, even in itsgeneral form stated above, is that--despite being an intuitively graspedand independent parameter set-- the three variables stated are also moredirectly transformed into device-language instructions. That is, theseparameters are more directly correlated with pigment information.

As a result the color information coded in this fashion (so readilysuited to color-compensation operations) can also be used in thedevice-control means. In other words, the information in this parameterset can be applied with relative directness to driving both therendition stage and the pigment-delivery subsystems.

As will be seen, this advantage survives, to an extent, even in systemsrequiring translation of the control signals into some other color space(e.g., RGB) for transmission to the device, followed by retranslationback into the specific parameters that drive the actual subsystems ofthe device.

A particularly remarkable result arises from the ready adaptability ofthis parameter set for use both as a perceptual color-manipulation spaceand as a rendition space: this dual adaptation in effect enableshalftoning to be conducted in a perceptual space.

Consequently colorant choice at each pixel can be manipulated in termsof input color, rather than after resolution into pigment terms. Takingadvantage of this capability, the system then can be made to preventrendition-derived color artifacts--such as pixels of pigment that areirrelevant to the desired color.

It is important to recognize at the outset that Fraction-Colorant andFraction-Black, although closely related to the Munsell concepts ofchroma and value, are not to be regarded as identical conceptualequivalents of those concepts. The invention derives from a return tofirst principles, and development of an entirely new way ofconceptualizing color.

Some part of the inadequacy of the prior-art machine systems, discussedearlier, arise as defeated expectations. That is, they come from auser's reasonable belief that the control knobs or computer-screen menuselections really correspond to abstract "lightness" or "vividness".

This is not to say that all of that prior-art inadequacy is triviallysemantic--i.e., merely a failure to put meaningful words next to theoperating controls. The problems of those systems cannot be cured bymerely describing to the user what the controls really do.

The reason is that in the actual working of each control the levels ofabstraction used are simply too great to be grasped by most users. It isnot the parameter names (e.g. "saturation") but their distorted physicalsignificance--chroma corrected for lightness, or saturation normalizedto the system gamut but symmetrical relative to the midlightnessplane--that is intellectually unmanageable.

This will be demonstrated fully in a later dissection of how the earliersystems operate. The parameters of the present invention, however--beingquite acceptable to users at a rudimentary level of color understanding,and also being comprehensible correctly at that level--create userexpectations which can be satisfied rather than defeated.

Thus the first aspect of the invention even in its broadest or mostgeneral form does resolve most of the prior-art problems introducedearlier. Nevertheless for fullest enjoyment of its inherent benefits thefirst aspect of the invention is preferably practiced in conjunctionwith certain other features or characteristics.

In particular, the foregoing text points out that the programmedinformation processor is for producing the effect of the resolving,performing and expressing steps enumerated above. Preferably theprocessor actually comprises neither means for directly so resolving theinformation nor means for directly performing the color-compensationoperations.

It is preferred that the processor instead comprise means for selectingvalues from a reference table, prepared in advance for a large number ofdesired colors, to produce the resolving-performing-and-expressingeffect. This shortcut permits use of a processor with far more modestcapabilities, and yet completes the entire process in a small fractionof the time--perhaps a thousandth of the time.

The reference table incorporates the influence of the resolution intosubstantially hue, Fraction-Colorant and black information. The tablealso incorporates the influence of the color-compensation operations,and expression of control signals in a form applicable to control thedevice.

The information processor comprises means for selecting values from thereference table to produce the resolving-performing-and-expressingeffect. In addition, it is further preferred that the table-definingmeans in turn include some means for defining not one but two or morereference tables.

One reason for this last-mentioned preference is that the apparatus canbe for use with any one of a plurality of different types of visiblemedium. For instance, if the device is a machine for printing on sheetmedia, the different types of medium may be plain paper, glossy paper,vellum paper or some other special type of paper, or transparent plasticsheet for making color transparencies.

In this case, the table-defining means comprise means for defining aplurality of tables, each as described for the single table above. Hereeach table further incorporates the influence of use of the apparatuswith a respective one of the plurality of different types of visiblemedium.

Another reason for the desirability of defining more than one table isthat the device-control means may comprise some means for performingcolor rendition--so-called "halftoning"--using any one of a plurality ofdifferent halftoning styles. In this case each table incorporates theinfluence of using a respective one of the plurality of halftoningstyles.

It is preferred to provide tables that incorporate the effects ofcrosscombinations of different halftoning styles and different media.

In addition, advantageously different tables are provided to incorporatethe effects of different color-control decisions. Preferably, forexample, an operator may wish to have the discretion to select betweenprinting color (1) substantially as it appears on a display screen or(2) with a clear, straightforwardly comprehended color modification.

Such modification can be incorporated in a particularly efficaciousmanner using the present invention. As already noted thehue/Fraction-Colorant/black parameter set is especially well adapted toperceptually meaningful color adjustments--which can then becommunicated efficiently and effectively to a device.

Thus preferably it is desirable to provide the user with a capability tomake the printout, for example, more vivid than substantially appears onthe display screen. With reference to the earlier discussions ofprior-art color spaces, it will now be appreciated that the user willexpect such increased vividness to be obtained without change ofblackness or hue.

In the hue/Fraction-Colorant/black parameter set, precisely such achange can be obtained by increasing the Fraction-Colorant without anyother change. Fraction-Colorant corresponds very closely to vividness ofperceived color, though not to the artificially defined "saturation"parameters of either the HLS or HSV system used heretofore.

This enhanced capability of a color device can be effected using thetable-look-up configuration already described. In this case differenttables are provided for different color-control decisions.

Thus pursuing the example of increased vividness, each tableincorporates the influence of using a respective one of a plurality ofdifferent Fraction-Color settings. Preferably tables are providedincorporating the influence of crosscombinations between differentFraction-Color numbers, different media and different halftoning styles.

It is found that providing just a single increased-vividness (higherFraction-Color) setting represents a substantial enhancement in thecapability of a sheet-medium color printing device. This enhancement isvery cost-effective; it is obtained at the incremental cost of onlydoubling the number of crosscombination tables.

In a second aspect of the invention, still within the first group, theapparatus is again for use with a visible medium. Here it is specifiedthat the medium is capable of visible-light projection.

This word "projection" is hereby defined for purposes of this document,and particularly for use in certain of the appended claims, in a specialway. The term shall be understood to encompass both reflection and alsoother ways in which media can interact with light.

One example of such other modes of light interaction istransmission--relating to situations in which a medium (e.g.,transparent plastic sheeting or another type of visible medium) afterbeing colored is viewed in transmitted rather than reflected light.Another example is emission, relating to situations in which a sheet orother medium is made to appear colored through use of, for example,phosphorescent or fluorescent substances; etc.

The apparatus of the second aspect of the invention also is for use withinformation from a color-image source that defines a desired color forat least one particular region of the medium. The apparatus comprises adevice for causing such particular region to appear colored.

That device, in turn, includes at least these elements:

(1) some means for causing the particular region to selectively projectvisible light of an associated first device-primary color--and for usein connection with this color exclusively, and

(2) some means for causing the particular region to selectively projectvisible light of an associated second device-primary color--and, again,for use with respect to this color exclusively.

For some definiteness in referring to these two elements, thefirst-mentioned one will be called "a first device-primary means"; andthe second, "a second device-primary means". It is not intended tosuggest that no more than two "device-primary means" are allowed;therefore in certain of the appended claims there appears the language"at least a second device-primary means".

The word "project" is to be understood in the same sense as the relatedform "projection" defined above.

A device-primary means may typically be embodied as a subsystem fordischarging colorant, or for actuating or stimulating a predeposited orembedded colorant to actually become colored, and so on. Many differentkinds of means for causing the particular region to selectively projectvisible light are contemplated within the scope of the invention.

Both the first device-primary means and the second device-primary meansare "exclusively" for causing the particular region to selectivelyproject visible light of a respective device-primary color--namely, thefirst such color and second such color, respectively. The word"exclusively" thus is to be read only as limiting the color which thedevice-primary means causes the region to selectively project.

Thus the word "exclusively" is not to be interpreted as a limitationthat the device-primary means must have no other ancillary functions. Tothe contrary, the device-primary means may indeed have other functions,such as interlocks for generating automatic alarms when colorant isexhausted or when a colorant discharge system is clogged,quick-release-and-insertion mechanisms, etc.

The apparatus also comprises a programmed information processor forreceiving the desired-color information, generating device-controlsignals for the device, and producing--once again--a complex effect.Here the effect produced by the processor is expressed in four parts:

A. First, the effect includes resolution of the desired-colorinformation into substantially at least:

(1) Fraction-Colorant information, namely the size of exclusively thechromatic fraction of the desired color, said Fraction-Colorantinformation being determined substantially directly from suchdesired-color information, and

(2) hue information;

B. Second, the effect includes color-compensation operations upon theso-resolved information. The effect includes taking into account knownFraction-Colorant-distortion-introducing and hue-distortion-introducingcharacteristics of other parts of the apparatus.

One such part of the apparatus is the color-appearance-causing device.Another part of the apparatus is device-control means which will bedescribed shortly.

This second part of the effect includes color-compensation operationsthat take into account the distortion-introducing characteristics togenerate at least these two types of information:

(1) new Fraction-Colorant information that tends to nullify introductionof such Fraction-Colorant distortion, and

(2) new hue information that tends to nullify introduction of such huedistortion.

The new hue information consists of at least these three hue-informationelements:

(a) identification of a particular one of the device-primary colors toserve as dominant primary for the particular region,

(b) identification of a particular other of the device-primary colors toserve as subordinate primary for the particular region, and

(c) the subfractions of the Fraction-Colorant to be allocated to thedominant and subordinate primary respectively;

C. Third, the effect includes generation of the previously mentioneddevice-control signals for the device, by:

(a) applying exclusively element (a) of the new hue-information elementsto generate a signal for selecting a particular one device-primary meansto supply the selected dominant primary,

(b) applying exclusively element (b) of the new hue-information elementsto generate a signal for selecting a particular other device-primarymeans to supply the selected subordinate primary, and

(c) applying exclusively the new Fraction-Colorant information andelement (c) of the new hue-information elements to generate signals formodulating the operation of exclusively the device-primary meansselected to supply the identified dominant primary and exclusively thedevice-primary means selected to supply the identified subordinateprimary, respectively.

As will be recalled, element (c) of the hue elements is the subfractionsto be respectively allocated to dominant and subordinate primary. Thusthe effect includes application of these subfractions to develop signalsfor controlling the corresponding device-primary means, respectively.

D. Fourth, the effect includes expression of the device-control signalsin a form applicable to control the device.

In addition to the device and the programmed processor, the apparatus ofthis second facet of the present invention comprises some means forreceiving the device-control signals, and applying them to actuate thedevice. These "device-control means" receive the signals from theprogrammed information processor in the control-applicable form justmentioned.

The device-control means also apply the control signals to implement theeffect produced by the programmed processor. In particular thedevice-control means apply the signals to effectuate the dominant- andsubordinate-primary selections, and the exclusive modulation, which areparts of the effect produced by the processor.

The foregoing may be a description or definition of the second aspect ofthe invention in its most general or broad form. Even in this inclusiveform, however, it can be seen to resolve the problems of the priorsystems discussed earlier.

Generally most of the comments made in reference to the first facet ofthe invention apply as well to this second facet. Further specificbenefits, however, can now be seen.

In particular, here it is made explicit that the system operates withrespect to regions of the medium. This phrasing points up the fact thatcolor decisions for different parts of a medium may differ--but at thesame time suggests that they need not.

For example, if desired Fraction-Colorant and Fraction-Black might beset for an entire graphic, and only hue varied for different regions.Alternatively, hue and Fraction-Black might be set across the frame, andvarious regions distinguished exclusively in terms of Fraction-Colorant.

Further the invention as practiced in its second aspect explicitlyproduces the effect of correcting for known distortions ofFraction-Colorant, as well as hue, arising in the device and the controlmeans--both stages being "downstream" from the compensation. In theprocess new values of Fraction-Colorant (and hue) are generated thattake into account the anticipated distortions.

Even more specifically, the new hue information includes thesubfractions of the Fraction-Colorant to be allocated to each of the twoprimaries that are active in each pixel. When applied to theFraction-Colorant for the corresponding pixel, these subfractions yielddesired quantities of the two primaries that are active at each pixel.

Because these effects are worked out in terms of Fraction-Colorantrather than in terms of, e.g., "saturation" as defined in prior-artsystems, the hue and Color-Fraction distortions tend to be nullifiedmore directly and effectively. The Fraction-Colorant variable offers abetter-correlated link between perceptually desired corrections anddevice commands.

As a practical matter, the device is typically driven through arendition stage, but as already mentioned that is not as remote arelationship when using the present invention as heretofore. It will beseen that other aspects of the invention--particularly relating torendition methods--are more effective in making use of this closelinkage than other types of rendition systems.

A preferred operation of the rendition driver according to anotheraspect of the invention will be discussed shortly. Within that renditionsystem, as will be seen, received information that calls for any inputcolor (for example the dominant primary) is actually routed, saved inmemory as required, and eventually applied to control the singlecorresponding device-primary means and no other.

Hence the better perception-to-machine correlation provided by theFraction-Colorant variable is not merely an abstraction but can beactually carried into effect as an advantage of the invention.

As with the first aspect of the invention, however, not only is itadvantageous to practice the invention in its broadest or most generalform but it is particularly beneficial to incorporate further featuresor characteristics. Features that enhance performance include thefollowing.

It is preferred that the color-appearance-causing device furthercomprise some means exclusively for causing a substantially achromaticsuppression of a specified fraction of the visible-light projection ofsuch particular region. These means will here be called the "gray-scalemeans".

In addition it is preferred that the programmed information processorfurther comprise means for producing the effect of:

A. also isolation from the desired-color information of Fraction-Blackinformation--namely, the desired fraction of the substantiallyachromatic suppression,

B. color-compensation operations upon the Fraction-Black informationtoo, taking into account known Fraction-Black-distortion-introducingcharacteristics of at least the device and the device-control means, togenerate new Fraction-Black information that tends to nullifyintroduction of such Fraction-Black distortion,

C. generation of further device-control signals--by applying exclusivelythe new Fraction-Black information to generate signals for modulatingthe operation of exclusively the gray-scale means, and

D. expressing the further device-control signals in a form applicable tocontrol the device.

In this preferred form of the second aspect of the invention, thedevice-control means also receive from the programmed informationprocessor the further device-control signals in that control-applicableform, and apply them in the form to actuate and control exclusively thegray-scale means.

Thus the handling is of black information is parallel to that of thechromatic information. With addition of this independent processing ofblack data, however, arises a triad of striking and important newcapabilities:

(1) First are the benefits directly paralleling those of the chromaticanalysis above. Black is an independent parameter in the color spacehere described, and as will be shown this is perceptually intuitive--butin addition it is an independent element of the machine space.

Thus again there is a close link between the terms in whichdistortion-causing mechanisms are nullified--and other perceptualmanipulations are effectuated, if desired--and the terms in which thedevice is controlled. This close nexus between perceptual and machinespaces yields a particularly powerful element of control to both thedesigner and the user.

(2) Second, independent handling of Fraction-Black information opens anopportunity to avoid the practice of representing blacks and grays bysubtractive combination of chromatic colorants. That practice is bothwasteful and inaccurate.

As will be seen, this opportunity is employed to particularly greateffect in this enhanced form of the second aspect of the invention.Fraction-Black is derived very directly and accurately from the inputdesired-color information, at the very outset.

Hence the throughput from desired black to device black can be bothextremely efficient in pigment usage and very linear. That throughput isinterrupted only to nullify known distortions and to introduce desiredmodifications based on esthetic preference.

(3) Third, this handling of black information, in conjunction with thepreviously discussed concept of Fraction-Colorant information, producesan even more striking benefit. Subtraction of these two fractions fromthe totality of color available to the eye yields explicitly thequantity or size of one remaining colorant fraction: white.

Accordingly the present invention offers an opportunity to use thecombination of the segregated black and white signals to effect simplenavigation about the color space. The following describes how these twosignals, either separately or collectively contain specific informationrelating to color space extremities.

The color triangle, or hue page, is formed by two lines: (1) theline,connecting white to the most saturated color--actually a color linewhere black is equal to zero; and (2) the line connecting black to themost saturated color--actually a color line where white is equal tozero. These two lines represent the outer perimeter of the color gamut.

Colors that are represented on the upper line, or upper gamut surface,may be accessed by simply clamping the black portion of HPG to zero. Thelower gamut surface, or lower line, may be accessed by clamping thewhite portion of HPG to zero.

Thus in the vast majority of practical cases the system conserves on anearly ideal basis: (a) physical coloring substance, (b) actuatingenergy, and (c) operating time. At the same time the invention avoidsgenerating muddy grays, whites and blacks--with a trace of unbalancedcolorant peering through the blend.

With respect to the second aspect of the invention it should beclarified that the first and second device-primary means each may bephysically either a single unitary subsystem driving a single pigment,color-emitting substance, etc.--or alternatively may be a pair of suchsubsystems. This clarification is mentioned to take account of thecommonplace need to effectuate primary colorants as, e.g., a subtractiveblend of two pigments, substances, etc.

For instance in a machine for printing inks on paper, the firstdevice-primary means may comprise a first device-primary color ink, afirst pen, and a corresponding actuating circuit. Alternatively the samemeans may comprise a first device-primary color ink pair, a first pairof pens, and a corresponding first pair of actuating circuits.

The analogous statements are also true for the second device-primarymeans. Whether the first or second device-primary means is a unitarysubsystem or a pair of such subsystems depends upon the desired color.

Generally in printing systems one of the two device-primary means isunitary and the other is a pair; and the first and second device-primarymeans normally share a particular one ink, pen and circuit.

These relationships follow from the fact that a desired hue, unless itis identically a primary colorant, is necessarily between two adjacentprimary colorants. Commonly in present-day machines (but notnecessarily) an even number of chromatic primaries is used, everyalternate one of which is present in the device physically as arespective single coloring substance.

In such systems, therefore, one of every two adjacent primariescorresponds to a coloring substance physically present in the device,and the other of the two is formed as a blend of two physically presentcoloring substances. All this will be more clear from the detaileddescription following.

In a third of its facets or aspects, the invention is apparatus forgenerating a hardcopy output corresponding to a representation on adisplay-screen device. This apparatus comprises a black-pigmentprinthead, and a plurality of different color-pigment printheads.

The apparatus also comprises some means connected to the printheads forselectively activating the black- and color-pigment printheads. Fordefiniteness of reference as above, it will be convenient to identifythese means as the "driver means".

The driver means in turn include some means for modifying componentinputs received from the display-screen device. These means will beidentified as the "color-compensation means".

According to this third aspect of the invention, operation of thecolor-compensation means is based on a color model having these threeparameters:

hue,

Fraction-Colorant, and

Fraction-Black.

Now this third facet of the invention, though once again expressedgenerally, has many advantages noted above for the other aspects. Itmore explicitly makes those benefits available for devices--such asprinting devices--that place pigment on a hardcopy.

It also more explicitly links those benefits to such devices that aredriven by applications programs employing color setup on a CRT, LCD orother color-display screen.

In a second group of aspects or facets of the invention, the inventionis a method.

Within that group, in its first aspect the invention is acolor-halftoning method for actuating a color-generating machine tocause a visible medium to appear colored. In particular the method isfor causing the medium to appear colored in correspondence withdesired-color information from a source of such information.

The method comprises several steps. The first step is receiving from thesource the desired-color information, and if it is not expressed inperceptual parameters then resolving that information into perceptualparameters.

Another step is then utilizing the information, while it is expressed interms of the perceptual parameters, to generate rendition-decisioninformation. The latter information represents a specific colorant ateach pixel location of the machine, respectively.

A further step is applying that rendition-decision information tocontrol the machine by selecting specific subsystems of the machine foractuation in relation to specific pixel locations, respectively.

The foregoing may constitute a description or definition of the firstmethod aspect of the present invention in its broadest or most generalform. Even in this form this facet of the invention resolves theobjectionable characteristics of prior halftoning systems describedearlier.

More particularly as will be recalled those earlier systems produce dotsof individual colors not individually related to the desired color.Although there is presumably some relationship when the entire array isviewed on some sort of averaged basis, the dot colors consideredindividually are irrelevant to the desired color.

A key to understanding this undesirable result can be found in onestatement in the prior-art section on rendition drivers. The propositionis that because a halftoning system must control decisions about machinecolorants, "naturally it operates in machine-colorant space."

The idea indeed is natural enough, but it lies at the root of theproblem. This mode of operation typically entails translation fromperceptual-space parameters to RGB or CMYK, preserving no identificationof the actually desired color.

In other words, downstream of that translation the system loses track ofthe perceptually desired input color. The rendition driver has onlyinformation about the machine colorants from which that input color isto be constructed.

Since the target color is unknown, the system must work with accumulatedresidual fractions of errors from various earlier pixels. Thesepropagated Floyd-Steinberg error numbers are unrelated to the perceptualcolor space used earlier in the color-compensation stage.

In fact these residuals from time to time do cumulate to colors not inthe original--and nothing constrains the system from actually printingany colorants which thus pop out of the error-residual diffusionprocess. At the end of the process, the resulting pixels are combinedfor evaluation only spatially on the visible medium and perceptually bythe observer--never within the rendition driver.

It is this mode of operation which leads to anomalous scatterings ofalien colors, particularly but not only near abrupt color edges orsmall, distinctly colored image fields. The blurred image edges andbleeding colors across such edges follow directly.

The invention as described above provides the means for correcting thisproblem: it operates in perceptual space. It does preserve informationabout the desired color, enabling use of that information to screen thecandidate colorants in the final colorant-selection process. In jargonof the present day such a process may be described as an ongoing"reality check".

Although the invention as described above thus enables resolution of theproblem, preferably the invention is practiced in conjunction withfurther features or characteristics that optimize its potentialbenefits.

In particular the invention in its first method aspect preferablyfurther comprises an additional step after the information-utilizingstep. That step is restating the specific colorant, at each pixellocation, in terms of machine parameters--if its perceptual expressionis not correctly interpretable as already being in machine parameters.

Here it is to be understood that the machine parameters corresponduniquely to separate physical coloring means employed by the machine.The applying step comprises addressing independent control signals toactuate separate subsystems of the machine which are associatedrespectively with the separate physical coloring means.

These subsystems further are controllable with respect to the pixellocations. In consequence the method effectuates a specific assignmentof the separate physical coloring means to each pixel location.

It will be seen that there is a further key to especially effectiveapplication of the perceptual information to drive the color machine.That key is selection of a particular perceptual language that has anadequately close relationship with those signals--that is to say, withthe language of the machine.

In addition it is preferable that the information-utilizing stepcomprise a further substep, performed after generating therendition-decision information for each pixel. It consists of alsodetermining for that pixel a resulting color error expressed in terms ofthe perceptual parameters.

Moreover it is preferable that the information-utilizing step comprisesa further substep, performed after the error-determining step for eachpixel. That step is distributing the color error, expressed in terms ofthe perceptual parameters, to other specific pixels for which theinformation-utilizing step has not yet been performed.

Also it is preferable, after the error-distributing substep, to laterperform the rendition-decision generation and then the error-determiningsubstep and then the error-distributing substep many times cyclically inthat order but with respect to said other specific pixels. Before eachsuch later performance of the rendition-decision generation, it isdesirable to first incorporate into the desired color, for that pixellocation, said color error distributed to that pixel from other pixelsfor which the error-distributing step was performed previously: thiserror-incorporation is to be performed in terms of the perceptualparameters.

A second facet or aspect of the method of the present invention is alsoa color-halftoning method for actuating a color-generating machine. Themachine is actuated to cause a visible medium to appear colored incorrespondence with desired-color information from a source of suchdesired-color information.

The method comprises the step of receiving from the source thedesired-color information, and resolving the information intosubstantially hue, Fraction-Colorant and gray. This resolving functionis performed only if the desired-color information is not already soresolved.

The hue, Fraction-Colorant and gray are expressed in terms of fractionsof four active colorants, which are defined for each pixel location ofthe machine as:

dominant primary,

subordinate primary,

black, and

white.

The second method aspect of the invention further comprises the step ofthen utilizing the information, while it is thus resolved substantiallyinto hue, Fraction-Colorant and gray, to generate rendition-decisioninformation. The rendition-decision information substantially representsspecific desired hue, Fraction-Colorant and gray at each pixel locationof the machine.

The rendition-decision information comprises a selection, for use ateach pixel location, of a respective single colorant that can beimplemented on the machine.

The invention in this aspect includes the further step of thendetermining a dispersable error resulting from use of said singlecolorant instead of substantially said desired hue, Fraction-Colorantand gray. A still further step is then dispersing said errorsubstantially in terms of hue, Fraction-Colorant and gray to selectedother pixel locations that are nearby.

Furthermore practice of the invention in this second method facet alsocomprises the step of--after the information-utilizing step--applyinginformation related to the single selected colorant to select andactuate one or more specific corresponding subsystems of the machine.

Once again, while the foregoing may represent a description ordefinition of the invention in broadest or most general terms, even insuch terms it can be seen to resolve all the difficulties of the priorart. Generally the above comments about the resolution of thosedifficulties by the first method aspect of the invention are applicablehere as well.

Furthermore, interacting very beneficially with the favorable effects ofthat first aspect are advantages of the particular parameter setemployed here. Simply because these parameters form a particularlyadvantageous perceptual space--by virtue of its parametric independenceand its intuitive character--the fundamental thrust of the first aspectof the invention is effectuated in a particularly satisfactory way.

The second method aspect of the invention goes well beyond that advance,however. The salient benefit of this facet of the invention resides inthe very direct relation between the hue/Color-Fraction/gray color spaceand the machine parameters.

That is, once the work has been done in terms of perceptual parameters,little is lost in the translation to machine operation. That is, infact, because very little translation is needed.

Again it is preferable for optimum enjoyment of the benefits of theinvention to incorporate certain other features or characteristics. Forexample, it is preferred that the error-determining step compriseexpressing the dispersable error in terms of fractions of the primarycolorants.

For purposes of expressing the second method aspect of the invention,the primary colorants are defined as:

the chromatic colorants, and

black, and

white.

It is further preferred that the error-dispersing step comprisecontributing a portion of each of the dispersable primary-colorant errorfractions to each of the selected other pixel locations, respectively.Preferably this contribution is performed substantially in accordancewith a geometrical weighting pattern.

Also the method preferably comprises the further step of cumulatingseparately for each primary colorant, for each said other location, theerror contributions from all pixels contributing thereto. In additionthe utilizing step preferably comprises, in generating therendition-decision information for each particular pixel, thesesubsteps:

further determining, from the desired-color hue, Fraction-Colorant andgray, these additional elements of the desired color:

(a) identification of the desired dominant and subordinate chromaticprimary colorants, and

(b) the desired fractions of all four active colorants;

then, for that particular pixel, adding the desired fractions of thefour active colorants to that pixel's cumulated errors for thecorresponding four primary colorants, respectively, to determine fourrespective composite errors for that pixel before printing; and

then making a decision to print, at the particular pixel, that one ofthe four active colorants which has highest composite error.

As can be appreciated this preferable mode of operation has the effectof actually constraining the information-utilizing step using theperceptual information.

A third method aspect or facet of the invention addresses a constraintprinciple independently, and without reference to use of a perceptualcolor space. More specifically, the third method facet is similarly ahalftoning method for actuating a color-generating machine that employsa plurality of colorants, to cause a visible medium to appear colored incorrespondence with desired-color information from a source.

The method comprises the step of receiving from the source thedesired-color information. It also comprises the step of then utilizingthe information to generate rendition-decision information representinga specific colorant at each pixel location of the machine, respectively.

This information-utilizing step includes these two substeps:

expressing the desired-color information in terms usable forconstraining the number of colorants employed by the machine, and

constraining the generation of rendition-decision information to selectonly colorants having at least some specified degree of relationship tothe input color expressed in said terms.

In addition the method includes the step of applying that generatedrendition-decision information to control the machine. Morespecifically, it applies that information to select specific subsystemsof the machine for actuation in relation to specific pixel locations,respectively; and actuate those specific substances in relation tospecific pixel locations.

This general expression of the third facet of the invention wouldgreatly ameliorate the prior-art problems discussed earlier. Itspractice in conjunction with certain other features or characteristics,however, is preferred.

For example, preferably the degree of relationship mentioned above isthat the selected colorant at least be one of a limited number ofcolorants that would be used as component colors or primaries toconstruct the input color alone. As will be seen, if this condition isto have significance, there is in turn implied some further limitationon the choice of perceptual space, for some systems may utilizefractions of all available colorants to form colors.

For best results the most highly preferred mode of practicing theinvention is to incorporate all of the several above-presented apparatusand method facets together in a single system.

All of the foregoing operational principles and advantages of thepresent invention will be more fully appreciated upon consideration ofthe following detailed description, with reference to the appendeddrawings, of which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an abstract representation of rectangular RGB color space;

FIG. 2 is a like representation of a mixed polar/altitude color spacecorresponding generally to HVC or hue-value-chroma space;

FIG. 3 is a like representation of an ideal color solid assuming aninfinite selection of ideal colorants, after Judd, op. cit. at 206;

FIG. 4 is a like representation of a generalized color solid for aninfinite selection of real primaries--just one per hue--id. at 214;

FIG. 5 is a like representation of four hue pages interrelating FIGS. 3and 4, and showing superimposed a constant-chroma cylinder, id. at 226;

FIG. 6 is a mixed graphical and mathematical representation of therelationship between RGB and HSV color spaces;

FIG. 7 represents an idealized or highly regularized hue page in the HSVcolor space--very generally analogous to any of the four FIG. 5 huepages--and including a showing of response in an HSV system to attemptsto obtain darker color exclusively;

FIG. 8 is a like representation showing response to attempts to obtainmore-vivid color exclusively;

FIG. 9 is a representation, analogous to FIG. 6, for RGB and HSL colorspaces;

FIG. 10 is a representation, analogous to FIG. 7, for the HSL system andshowing response to attempts to obtain lighter color exclusively;

FIG. 11 is a like representation showing response to attempts to obtainless-vivid color exclusively;

FIG. 12 is a diagrammatic representation of an error-diffusion weightingpattern used in the prior art and usable with the present invention;

FIGS. 13 and 14 are HSV hue-page diagrams like FIGS. 7 and 8 but withinternal lines of constant parameters S and V;

FIGS. 15 and 16 are like HLS diagrams for FIGS. 10 and 11 but withinternal lines of constant parameters S and L;

FIG. 17 is a representation analogous to FIGS. 6 and 9, for the HPGcolor model;

FIGS. 18 and 19 are diagrams like FIGS. 13 through 16, for an HPG huepage and increases in blackness and vividness;

FIG. 20 is a like diagram showing boundary behavior;

FIGS. 21 and 22 show computer simulations corresponding to thestructural parts of FIGS. 15-16 and 18-20 respectively;

FIG. 23 is a diagrammatic showing of the error-diffusion method asinformation movement relative to memory buffers;

FIG. 24 is a software flowchart for the same method;

FIG. 25 represents a clustered-dither color vector;

FIG. 26 is a block diagram of a color-reproduction system operatingalmost entirely with HPG parameters;

FIG. 27 is a similar diagram but with an existing input subsystemoperating with RGB signals;

FIG. 28 is a like diagram but RGB-interfaced throughout (except at theprinter);

FIG. 29 is a like diagram but showing look-up operations;

FIGS. 30 and 31 show the printing-machine carriage and pens inperspective and plan respectively; and

FIG. 32 is a schematic showing, in plan, of pen stagger.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In order to fully appreciate the operation of the present invention itwill be helpful to first understand the internal operations of the twoprior-art color spaces discussed in detail earlier. Unfortunately theprior art apparently has not provided an understanding of those colorspaces adequate to explain the very puzzling responses of those earliersystems to color-adjustment commands.

Only in the process of completing the present invention has it becomepossible to obtain a more-detailed understanding of the reasons forthose seemingly irrational responses. Therefore the explanations arepresented here rather than in the earlier prior-art discussion.

1. DEEPER UNDERSTANDING OF THE PRIOR-ART "HSV" COLOR SPACE

FIG. 13 is a representation of the same HSV hue page as in FIGS. 7 and8. Also included in FIG. 13, however, are nomographic lines within theinterior of the hue page--showing the internal structure of the colorspace.

In particular FIG. 13 includes not only the upper diagonal linerepresenting value V≡1, but also other interior lines 119 parallel tothat line and representing other constant values V; for each of theselines the associated constant-value numbers are fractions.

These additional lines of constant value V may be regarded asintersections between cones of constant lightness and the hue page.

Also drawn on the hue page are analogous internal lines 118 ofsupposedly constant vividness--but in any event constant "saturation" Sas defined in the HSV model. More specifically, these lines of constantfractional saturation S radiate at various angles from the black point,at the bottom vertex of the hue-page triangle.

The loci forming these various lines can be inferred from the RGB-HSVrelationship just discussed in reference to FIG. 6--or, morespecifically, from the mathematics commonly employed in workingintimately with the HSV system.

FIG. 13 reveals the color-space rationale behind the strange behaviorplotted in FIG. 6. When a user moves from a starting position byadjusting value V to decrease the lightness, the system constrainsmovement to a line of constant "saturation" S as defined.

Within the internal logic of the color space, this is sensible. The ideais that pure change of value V should hold "saturation" S constant.

Unfortunately, however, each such constant-"saturation" line, as seen inFIG. 13, is at some angle to the vertical. Therefore instead offollowing a desired vertical path 112, drawn dashed, the system insteadtakes the solid-line route 113 which follows a leftward-and-downwardinclined constant-"saturation" line S=0.6.

FIG. 14 discloses the similar rationale behind the peculiarities of FIG.7. Here the user moves from the starting position by adjusting S toincrease saturation--intending to move along an outward horizontal path114, again drawn dashed.

The system responds now by following 115 instead the downward-inclinedconstant-value line V=0.6 to a point of increased vividness butdecreased lightness. Once again the philosophy of independent variablessays that a pure change of the "saturation" variable S should hold thevalue variable V, as defined, constant.

The reader--but not the untutored user--perhaps can now predict that theHSV control system will interpret the instruction as a command toincrease saturation S as defined without changing value V. This meansoutward movement along a line of constant value.

All such lines, unfortunately, are angled downward and outward relativeto the horizontal. Therefore outward (toward-vividness) movementobtained with the "saturation" control alone is necessarily accompanied115 by downward (toward-darkness) movement.

If the user later tries to compensate by adjusting the lightness controlto move 116 vertically, the system responds instead by moving along aconstant-saturation contour 117, very roughly S=7/8 in the drawing.Because this is angled upward from the vertical, the attempt will alsorapidly increase the vividness.

The user would have to see and understand FIG. 9 to comprehend how tomaneuver from one desired point to another. Even then it would bedifficult, as will be shown momentarily.

In any event the user is not likely to be afforded such an opportunity.That would be tantamount to confession that the color-model which thedevice designers selected--presumably on purpose--to control the colordevice is an unfathomably nonperceptual one.

It was observed in the earlier discussion of FIG. 7 that the internalstructure of the HSV space will also confound the user's efforts toachieve mental calibration. This can now be seen easily by comparing thesensitivities, as seen in FIGS. 13 and 14 respectively, of vividnesschange to lightness change.

As mentioned earlier, the angle of the constant-saturation lines varieswith position within the hue page. In FIG. 14 the attempt to move upwardoccurs while the system is operating at a different point (lower) in thediagram, where the constant increments of lightness are spaceddifferently (further apart) along the constant-vividness lines thanpreviously.

This means that the S=0.8 line followed upward in FIG. 14 is angled evenmore from the vertical than the S=0.6 line followed downward in FIG. 13.Consequently the apparent vividness will increase much more rapidly nowthan it decreased in FIG. 13.

In order to reach the desired point at the tip of the horizontal outwarddashed arrow without iteration, the user would have to stop increasingvividness long before the apparent vividness reaches the desired visualeffect. It would be necessary to stop at a point just past the S=0.6line, and then move outward along an intermediate contour of roughlyS=0.7, to achieve the desired effect in only two manipulations.

Still another now-evident failing of the system arises at the bottomvertex, where all constant-saturation lines converge. Theoretically forthe HSV space the entire saturation range is compressed progressivelytoward zero as the system approaches the V≡0 pole--where by definitionsaturation S is indeterminate.

In this region, as in the HLS example discussed previously andelaborated below, the sensitivity of the system to adjustment ofsaturation S differs drastically from that found in the middle to highrange of V.

2. DEEPER UNDERSTANDING OF THE PRIOR-ART "HSL" COLOR SPACE

FIG. 15 is a representation of the same HSL or HLS hue page as in FIGS.10 and 11. FIG. 15, however, includes interior nomographic lines (as inFIGS. 13 and 14) to display the internal structure of the HLS space.

In the example previously discussed with respect to FIG. 10, theobjective was simply to move upward along a vertical line (a dashed lineas illustrated) from approximately lightness L=0.35 to L=0.75. Asbefore, the control system demands that such a pure-lightness maneuverfollow a line of constant "saturation" as defined.

All such lines 218, 218' within the solid have shapes similar to, butnested within, the two outer-surface lines discussed already in theprior-art section. The family of constant-S lines accordinglycorresponds to intersection of the hue-page plane with a family ofdouble opposed cones, each such surface representing a three-dimensionallocus of constant "saturation".

Hence as a "lightness" control is operated in one direction to moveupward 212, for example, from the L=0.35 plane below midlightness to theL=0.75 plane below, the system moves along the astounding path215-217-217' shown (in solid arrows).

First it moves outward along the constant-"saturation" S=0.75 line 215,angling toward the midlightness line L=0.5 upward and outward shallowly.Then it reverses field abruptly to angle upward and inward shallowlyalong the upper continuation of the same line 217 of so-called"constant" S=0.75.

Notwithstanding that this entire movement follows what is interpreted asconstant "saturation", the apparent vividness very evidently undergoesexcursions that can only be described as bizarre. This can be fullyappreciated upon taking into account that the lightness controlcontinues to be operated relatively slowly in the same direction.

Given the starting position and the ending lightness number (L=0.75)selected for the FIG. 10 and 15 example, the apparent vividness actuallycrosses over 217' its original level (corresponding to the position, inthe right-to-left direction, of the vertical dashed line). Even greatercrossovers are possible for other starting points.

Since all the illustrations of prior-art perceptual spaces have beendefined and drawn for perceptual uniformity--and that is indeed theirmajor claim to virtue--it is entirely fair to point out that these innerconstant-saturation lines are all at very shallow angles to thehorizontal. Hence the sensitivity of apparent vividness change todesired lightness adjustment is extreme, fully justifying suchpicturesque language as "bounds" and "dives".

The discussion will turn now to FIG. 16. Some additional understandingcan be gained for the earlier-described complex variations in theresponse of an HLS system to vividness adjustment at different lightnessvalues.

Here the system is relatively well behaved in the sense that nointerdependencies arise to deflect a maneuver from the naturallyintended course. Pure changes in saturation, even defined in thepeculiar fashion illustrated, correspond to movement 213 radially orhorizontally outward along lines of constant lightness L.

Along the way the condition of the system crosses many of thechevron-shaped lines of constant saturation, producing a change in bothdefined saturation and actually perceived vividness. The change isproportional to increments in input saturation-control signal.

Nevertheless in a comparison of vividness responses for differentlightness values, the system does not appear well behaved at all. TheHLS system declares that the full range of saturation values is obtainedin moving from the vertical lightness axis at the left edge of thediagram to either diagonal S=1 line at the right--regardless of positionalong the lightness scale.

The total perceived-vividness range, however, depends very strongly uponthe position along the lightness scale--e.g., whether the user is beingchauffeured along a short horizontal line 213' near top or bottom, oralong a long line that passes near the midlightness point. If themachine designer assigns all these different distances to the samenumber of bits in a manual control system, resulting system response issure to bewilder any ordinary user.

For example, suppose that movement along the solid rightward arrow atlightness just below L=1/2 (actually about 0.45), is made to use abouthalf the full range of adjustment. This would be expected by comparingthe length of the arrow with the full width of the hue page at thatL=0.5 lightness level.

The small arrow at about lightness L=0.9 is much shorter, but as can beseen it is some two-thirds the width of the hue page at that near-apexlightness level. Therefore adjusting saturation by substantially morethan the amount required to traverse the entire length of the lower,longer arrow will not suffice to move the length of the higher, shorterarrow.

Furthermore, operating the same control through two-thirds of its entirerange (a patience-testing exercise for some types of equipment) would berequired to take the system to the limit of maximum "saturation" asdefined--i.e., to the S=1 envelope line. Once again, however, forreasons presented earlier the "saturation" parameter S correspondspoorly to vividness as perceived.

Thus in the present case, even driving the system to thatmaximum-saturation limit line would only produce a very low vividness.Specifically, it would be that vividness associated with the distance ofthe arrow tip.

That is the distance from the zero-saturation W-K axis to the S=1diagonal, at the L=0.9 lightness level. This amounts to only perhaps onthe order of one-quarter the full vividness range, as can be estimatedfrom the drawing.

If system designers attempted to correct by placing a normal adjustmentrange in the neighborhood of the lightness level identified by thehorizontal dashed line, then as mentioned earlier the operation verynear either top or bottom vertex of the drawing still would beirrational. Furthermore the system would be overly responsive to thecontrol adjustment nearer midlightness--as, for example, to obtain theadjustment suggested by the longer arrow in FIG. 16.

3. THE NOVEL HUE-PLUS-GRAY COLOR SPACE

This invention returns to first principles for development of anentirely new color-management tool. The Hue-Plus-Gray (HPG) Color Modelestablishes a mechanism for direct controlling reproduction of theentire color palette of a color-reproduction process.

HPG incorporates the concept that renderings of a specific hue may becompletely achieved by combining a quantity very closely related to thechroma of that hue with various levels of gray--hence the name Hue PlusGray.

Hue Plus Gray is simultaneously a color space, a machine-space colorvector, and a color-control concept that increases color control. It isa polar coordinate space and is designed to be consistent with thetriangular shape of color palettes.

It is a particularly good color space because, for example, pale colorsare never said to have full (large) saturation values. More generallyspeaking, the model is entirely well behaved near all its limit linesand vertices.

It is a particularly good machine space in that actual quantities ofpigment put down are represented directly by color-spaceparameters--allowing even the rendition stage to be driven verystraightforwardly in terms of the input desired color.

It is a particularly good color-control concept because it possessesbetter parametric independence than at least prior industrially appliedperceptual spaces, and also because it satisfies reasonable intuitiveexpectations. That is not to say that the working parameters of HPG areprecisely congruent with, for example, Munsell's HVC--for they are not.

As pointed out several times already, however, the invention returns tofirst principles. It is believed that a parameter set which possessesall the other striking advantages set forth here, particularly includingreasonably intuitive definitions, can make slight deviations fromclassical concepts harmlessly.

This color model establishes a straightforward relationship betweenperceptual space and the color-delivery mechanism. In this model, coloris divided into its two major components: chromatic and achromatic.

Each of these components in turn is subdivided into two respectivesubcomponents. The chromatic component is divided into two fractionalcomponents consisting of two colorants--sometimes called a primary and asecondary, but in this document more commonly called dominant andsubordinate primaries, or dominant and subordinate primary colorants.

a. The chromatic component: control of hue and chroma

In this model, hue is controlled by combining only two colorants. Thehue coordinates of the two colorants determine the range of hues can bereproduced by those two colorants. Specifically, the range is restrictedto only those hues positioned between the hues of the two colorants.

As an example, hues that range from colorant 1 (here abbreviated "C1")through colorant 2 ("C2") may be achieved by applying quantities of C1and C2 in which the fractional amounts of each range between zero andone, in inverse relationship, but summing to one.

Two favorable results are achieved by restricting the hues to thosewhich are between the hues of the two colorants employed:

(1) Doing so removes any possibility of reproducing a hue by usingcolorants which are further away from the desired hue. At the renditionstage, this removes the possibility of hue artifacts common to errordiffusion.

(2) Doing so also increases the ability to control hues, reducing hueerrors--simply because the controlling hues are closer to the targethue.

In this model, hue can be correlated as a function of the fractionalcomponents.

Chroma is directly proportional to one coordinate of the HPG system,namely the quantity of colorant present. Chroma is controlled bycontrolling the quantity of colorant applied to the medium.

Chroma is dificult to control when based only on the chroma of theprimaries and secondaries (or colorants). For pixel-based color printingmachines the colorant in each pixel overlaps slightly with the colorantfrom adjacent pixels.

The resulting chroma is determined in part by the effective chroma forthe hue that arises from mixing of the two colorant where they overlap.This effective chroma differs from the superposition or average of thetwo or several chromas nominally established by the apparatus for theprimaries and secondaries in use.

In this model, the chroma component of HPG can be correlated orcontrolled as a function of hue. This control can be effected in such away as to make allowance for pixel mixing of colors.

b. The achromatic component

Conventionally, as described earlier, the achromatic component of coloris described by a single variable, value V or lightness L. Achromaticcolors, called grays, are measured by using intermediate numbers alongthose scales between the high and low extremes white W and black B or K.True grays have no chroma or zero chroma, and no hue or indeterminatehue.

In the HPG system the control of value is achieved by controlling thequantity of gray to be applied. In turn, a specific gray is achieved bycontrolling the quantity of black used--for example, in a color printingmachine the amount of black pigment applied in the presence of white.

In this model, the quantity of black is also a coordinate of the system.Thus the gray component of the color can be controlled or established.

c. The parametric concept

The complete HPG model now will be described in terms of its individualparametric components. The color space is described fractionally so thatit can be easily scaled to the color primaries of any specific deliverysystem.

It is also forward-compatible to machine systems which used grayscaledcolorants or which otherwise increase the number of system primaries.For example the system is readily adapted to drive machines in which anorange pigment is added to CMYK.

The color space is divided into two components: the fractional part Fcwhich is chromatic and the fractional part Fa which is achromatic--i.e.,gray. In this document the chromatic fraction is also called"Fraction-Colorant" and denoted by the symbol N. The sum of thechromatic and achromatic components produces unity:

    Fc+Fa≡N+Fa=1.

The chromatic portion Fc=N is the principal parameter for control ofchroma. It is further subdivided into two components C1, C2 to controlhue. The fractional parts Fc1 and Fc2 required for hue control arerequired to fill the chromatic space:

    Fc1+Fc2=Fc≡N.

The achromatic or gray component Fa is further divided into twocomponents to control value. The fractional parts of black K and white Ware required to fill the achromatic space:

    Fk+Fw=Fa.

In this document the variable Fk is called "Fraction-Black" and alsodenoted by the symbol K.

The complete model of any color can be expressed as:

    Fc1+Fc2Fk+Fw=1.

This form is called an HPG vector and is in a form suitable forhalftoning either by ordered dither or error diffusion. This formulationallows control or so-called "printing" of white--in a machine thatprints on substantially white media--as the difference Fw=1-(Fc1+Fc2+Fk)or 1-(N+K).

The HPG model is consistent with many color-reproduction processes.Compatible processes include thermal ink, thermal transfer, xerographic(sometimes called "electrostatic"), CRTs and others.

The application of principal immediate interest is the thermal inkdelivery system with CMY pens producing the chromatic portion and ablack pen producing the gray portion of the color. Such systems includethermal-inkier devices manufactured and sold by the Hewlett-PackardCompany, headquartered in Palo Alto, Calif.

In such devices the chromatic parameters of the HPG model are applied todrive the color pens. The gray portion, in terms of just the singleparameter Fraction-Black Fk≡K, to drive the black pen.

The HPG system permits direct control of the three major colorattributes--value or lightness, hue, and chroma or vividness. (Referencehere is intended to the fundamental and intuitive HVC concepts ratherthan to their adaptations as parameters, sharing the same names, in thedeficient prior color spaces that have been implemented commercially.)

Value or lightness is controlled by applying gray fractionally, e.g. bydelivering black on a white medium. Hue is controlled as relativefractional proportions of two colorants--and chroma is controlled byapplying this hue (i.e., actually by applying each of the two chromaticfractions) fractionally.

More specifically, hues are created using fractional combinations ofadjacent dominant and subordinate primary colorants C1, C2. These areselected to most closely enclose the target hue.

The resulting color is shaded by inserting gray in place of some of thechromatic colorants--black to darken the color, white to lighten it. Thetotal amount N of chromatic colorant is directly proportional to theconceptual chroma parameter V in idealized Munsell HVC space.

Because of good correlation or consistency with color-reproductionprocesses, the HPG system variables HNK or their elements Fc1, Fc2, Fkcan be applied with little variation in the process devices. Because thecolor is coded in terms which apply directly to the delivery mechanism,the HPG parameters can be halftoned directly.

Improvements in use of higher-order systems such as error-diffusionsystems (as compared with clustered-dither systems for example) areparticularly notable--because such rendition systems are capable ofmaking fuller use of the benefits of the HPG space.

The HPG color space is particularly suitable for use with color-captureor color-reproduction systems--for example, systems in which a printingmachine is directed to reproduce on paper a color image that appears ona display screen. Most of such systems are strongly nonlinear.

The color-space characteristics of such systems, however, correlatenicely with the HPG parameters. This correlation allows for colorcompensation, which is a necessary step for achievement of overalldevice-independence in matching the resulting printed output color tothe desired input color.

Another feature of the model is that it facilitates a particularlystraightforward compensation for the amount of gray inphysically-available pigments. In other words the model might be said to"remove" the gray--more precisely, its effect--from the color component.

This is accomplished by adjusting the achromatic component Fa to specifyonly the additional amount of gray needed to achieve the intendedresult. (Of course this is fully effective only if the intended gray isat least equal to that in the pigments.) Analogous compensations arereadily made for hue impurities in any of the pigments.

d. Relationship to usual input-color parameters (RGB), in mathematicalform

At present, conversion from the traditional representation ofprinting-device color is necessary because operating systems for displaydevices and the like are not yet available in HPG coordinates. That isby no means considered a permanent state of affairs, for--as mentionedabove--the HPG model is fully compatible with at least most otherpractical devices.

Transformation from RGB space to HPG space, which is to say from thevariable RGB to the variables HNK, is performed using three expressions.This is to be expected from the three-dimensional nature of both spaces.

The expression for hue is the same as presented in the prior-art section(specifically, in part 2-d on the HSV space). The expressions forFraction-Color N and Fraction-Black K appear here:

    N=Max-Min

    K=1-Max.

In certain parts of this document the quantity Fraction-Black K isoccasionally simply called "black". Although there may arise from thatusage some slight confusion between the colorant black "K" and itsquantity "K", the usage has been adopted in certain passages to moreclearly emphasize certain other important relationships; and it isbelieved that the distinction will be clear from the context.

e. The same relations in graphical form

FIG. 17 shows the above-stated relationships graphically. It illustrateshow the new parameters N and K relate in an extremely straightforwardand intuitive way to traditional ways of talking about color.

This way of showing these relationships graphically--like those of FIGS.6 and 9 discussed earlier--is believed to be a novel form ofrepresentation. It is particularly helpful in comprehending thefundamental color-reproduction phenomenon.

FIG. 17 shows three input-color signals Max, Mid and Min. In theillustrated example, they happen to correspond to quantities Rin, Ginand Bin of colorants red, green and blue RGB respectively--but it isemphasized that this assignment is merely exemplary.

A first important fact that can immediately be seen from thisrepresentation is that the size Min (or, in the example, Bin) Of theweakest input color B represents a level of colorant that is present inall three of the inputs. That is to say, the quantity Min is present inall three desired-colorant levels in common.

Although the identification of the weakest input color as blue is justan example, the broader conclusion of the preceding paragraph is not. Inother words, the quantity Min is present in all three desired-colorantlevels regardless of the assignments of Max, Min and Mid to specificcolorants--or, even more simply, always.

This realization can next be connected with the well-known fact thatequal quantities of red, blue and green when blended produce the visualexperience called "white". The portions of RGB signal that are presentin common simply make white, and the amount of white is equal to thesize of the input signal Min always--irrespective of which colorant itis that has that signal.

Hence an HPG-controlled system can simply subtract that component ofcolor away at the outset, identifying the corresponding fraction as theamount W of white that is required. In a machine for printing on sheetmedia--most typically white--this is a particularly powerful initialstep, since as noted earlier white essentially comes free with thepaper.

With that step completed, the remaining analysis can focus upondetermination of colorant quantities to be actually deposited. Insystems (for instance, CRT systems) that do not entail what might becalled "free white", the great benefit just introduced is not enjoyedfully--but as will be seen shortly a corresponding advantage appears inits place.

Next attention turns to the gap, at the top of the diagram, between thefull-color level Full≡1 and the height Max of the strongest inputcolorant. This vertical gap is between the horizontal line across theextreme top of the diagram and the tallest bar, labeled "Max".

This gap corresponds to a fraction of the available dynamic range ofcolor--but it is a fraction used neither by white W nor by any chromaticcolorant RGB. The gap thus corresponds to absence of light--which is tosay, darkness or blackness itself.

The height of the vertical gap is accordingly labeled K. The diagramshows that it is equal to 1-Max, as indicated by the equations presentedin the preceding subsection.

In a printing system, black is not typically free--but ordinarily it isat least as economical as any chromatic colorant, and available in farmore pure or accurate form. Hence separating out the quantity K of blackfor separate handling results in a certain level of economy.

Far more importantly, this approach results in a great operatingefficiency and accuracy. The alternative for comparison consists ofattempts to construct black by subtractive combinations of othercolorants.

What is more, the corresponding advantage promised just above, for CRTsystems and others unable to obtain free white, now materializes. Inmost of those systems, there is a colorant which is free, and thatcolorant is black--or at least a very dark grey.

So far it has been shown that the HPG color model deals with thenonchromatic colorants KW in remarkably advantageous and remarkablysimple ways. The simplicity is in fact itself an additional advantage.

The same will now become clear for chromatic colorants as well. Sincethe foregoing discussion accounts completely for the achromatic elementsKW of the full color space, necessarily the remainder of the spacecorresponds to the chromatics.

As a starting point, the full color space extends vertically from thehorizontal line across the bottom of FIG. 17 to the like line Full≡1 atthe top. Whatever portion of this vertical distance is not used up byblack and white KW must necessarily be that remainder which correspondsto chromatics.

As seen in FIG. 17, the remainder is the vertical distance between thetop of the weakest desired-colorant signal and the top of the strongestone. That distance, shown in the drawing labelled N, corresponds to thedifference Max-Min; thus N=Max-Min, just as displayed in the equationsof the preceding subsection.

Now the upper portion of that central segment of the drawing, the partbetween the top of the intermediate-strength signal and the top of thestrongest, can be represented by just one colorant. That is thecolorant--in this document usually called the "dominant primary"--whosesignal is the strongest in the particular case at hand.

For the particular input color assumed in FIG. 17, the dominant primaryis red; however, once again the general statement is valid in everycase: the fraction of the strongest signal which is not common to theother two can be represented by a single colorant. That colorant isalways the one (whichever one) whose signal is in fact strongest of thethree.

The part of the drawing corresponding to that fraction is equal inheight to the difference Max-Mid. The HPG model sets the desireddominant-primary C1 output quantity Fc1 equal to this difference,Fc1=Max-Mid.

Assignment of this signal strength to the quantity of an output colorantis particularly straightforward in the present case since in manypractical systems the identification part of the assignment isessentially one-to-one. Specifically, the colorant with strongest inputsignal is identically the colorant used as dominant primary C1 in theoutput device.

The remaining portion of the full color space in FIG. 17 necessarilycorresponds to the portion of the Fraction-Colorant N strip which liesbelow the top of the input or desired-color signal of intermediatestrength. The vertical height of that portion is equal to N-Fc1, and socould be calculated using that expression--but the drawing shows thatsame quantity is also found from the input signals directly as Mid-Min.

The conclusion is that the amount of chromatic colorant yet to beprovided by the color-delivery device is

    Fc2=N-Fc1=Mid-Min.

It remains only to say what colorant it is that should be delivered inthis quantity. In this document that colorant is usually called the"subordinate primary".

FIG. 17 shows that the remaining chromatic colorant consists of parts ofthe two active color bars, "Max" and "Mid". One of these is the upperpart of the bar representing the intermediate-strength signal "Mid"; theother is the middle portion of the dominant-primary bar "Max" that hasnot already been assigned to drive printing of the dominant primary.

From the drawing it can be seen that these two adjacent color-space barsare of equal height, namely the height of that part of the bar for themidstrength input color which lies above the bar height for the weakest:Mid-Min. This is just the expression mentioned above for the strengthFc2 of the subordinate primary C2.

The desired color therefore consists of equal parts of twoprimaries--those whose signals are strongest and medium-strongestrespectively. What is wanted in fact is that same quantity Fc2=Mid-Minof a single colorant whose hue is the average of the hues of the "Max"and "Mid".

Exactly such an averaging combination of two equal parts of these twoprimaries can be provided by a single primary whose hue is substantiallymidway between the two. Such a single primary is attainable as can beseen from FIG. 2.

That drawing provides a reminder that the primaries RGB are spacedequally about the origin in terms of hue angle, and that three otherprimaries CMY occupy the alternating or in-between positions. A hueaverage for any particular two of the three primaries RGB thus is alwaysavailable in the form of that one of the other primaries CMY that isbetween those particular two.

FIG. 2 also shows what that subordinate primary will be for the FIG. 17example. Specifically, it will be the primary which is midway betweenthe red and green primaries which are strongest and next-strongest inthe example; that primary is yellow. In the general case, it is theprimary that lies between whichever two are strongest and next-strongest.

The primaries CMY for some purposes may be identified as "secondaries"or "complements"; however, for purposes of the present document it ismore useful to designate them simply as primaries. This nomenclaturehelps to emphasize that in a practical case any of the six RGBCMY can bethe strongest output colorant.

It should be noted that the output quantity of subordinate primary maybe either larger or smaller than the output quantity of dominantprimary. The matter turns only upon the relative heights of the "Max"and "Mid" bars.

If the "Mid" bar is nearly as tall as the "Max" bar, then the dominantprimary will be printed only in a much smaller quantity than thesubordinate primary. If the "Mid" bar is just barely taller than the"Min" bar, however, then the dominant primary will be printed in muchlarger quantity than the subordinate.

The subordinate primary, however, necessarily must always be one of thethree primary colorants (here CMY) that are not employed in expressionof the input color (here RGB). The subordinate primary always plays therole of supplying an average-hue colorant to represent the twoequal-height input bar segments of length Mid-Min.

Reference once again to the hue disc of FIG. 2 will suggest that anyinput color must either be (1) identically one of the primaries or (2)between two of the primaries. The latter case is far more common, or atleast more general; but the former case will also be stated.

If the "Mid" and "Max" bars have equal height, there is no dominantprimary--or, in any event, identification of a dominant primary isindeterminate and its output quantity is zero. In that case the entirequantity N of Fraction-Colorant will be applied to drive thesubordinate; as just noted, this will be one of the primaries CMYsometimes called "secondaries" or "complements".

At the other extreme, if it is the "Min" bar which has the same heightas the "Mid" bar, then there is no subordinate primary--or, if there isone, its identification is indeterminate and its output quantity iszero. Then the entire quantity N of Fraction-Colorant is used to drivethe dominant.

The foregoing comments may be compared with the earlier discussions ofFIGS. 6 and 9, representing the corresponding relationships between RGBand HSV/HSL spaces, to better appreciate the appeal of the HPG system.Such review will reveal that--within the simple graphical presentationof FIGS. 6, 9 and 17--relatively little or no meaningful physicalsignificance can be ascribed to the variables that constitute theprior-art parameter sets.

f. Color compensation and control in the HPG model

The now-preferred embodiment of the present invention provides onlyrelatively minimal color control as such, namely manual selectionbetween two discrete levels of vividness as noted in the earlier"Summary" section of this document. A great part of the capability ofthe current preferred embodiment is accordingly devoted to colorcompensation rather than control.

Nevertheless, the functions used in compensation, and the relativestraightforwardness or ease with which those functions can be performed,are to a significant extent the same as those used in color control.Further, a relatively full presentation of the deficiencies of prior-artcontrol systems on a color-control basis appears in earlier sections ofthis document.

Accordingly for completeness and to facilitate comparative understandingof the various systems a similar presentation will now be offered forthe HPG system. FIG. 18, like the analogous nomographic drawingsdiscussed earlier, is an idealized representation of a hue page--but nowfor the HPG system.

Here as in FIG. 7 the user's objective is assumed to be a darkening 313of the color from a starting point, namely the upper end of the arrowthat appears in the drawing. In HPG space, technically speaking, theperceptual or intuitive concept used actually is not darkening; ratherthe system operates in terms of blackening, or adding black colorant.

In purest principle thus it might be most satisfying conceptually ifmovement were perpendicular to lines 319 of constant Fraction-Black K.These constant-K lines 319 appear angled on the drawing--as are theconstant-value V lines in HSV space, shown in FIGS. 6, 13 and 14. Hencethese too correspond to plane-and-cone intersections.

An instruction to the system to decrease one variable (hereFraction-Black), however, as in the previous examples corresponds tomovement along a line 318 of constant implication for the othervariable--here, Fraction-Colorant N. Those lines 318 in FIG. 18 arevertical; hence the adjustment corresponds directly to vertical movementon the hue page.

Such a change fails to correspond to movement perpendicular to constantFraction-Black lines 319. This particular departure from technicalideality, however, may be at least considered advantageous, in that theresulting descent parallel to the W-K axis is intuitively interpretableas increasing the darkness--without any conceptual change relative tothe classical and intuitive HVC space.

Whether the movement is interpreted perceptually as darkening ortechnically as blackening, however, it will be found entirelysatisfactory. The reason for this statement is that in neitherinterpretation can there result any change of Fraction-Colorant N--or ofvividness. In this type of adjustment, both technical independence andperceptual independence of the two parameters are enjoyed.

FIG. 19 illustrates the converse situation: an attempt to increase 314vividness. Here the situation is more complicated and interesting.

The idealized HPG system interprets a demand for increased vividness orFraction-Colorant N as an instruction to move along a contour 319 ofconstant Fraction-Black K. As already noted, these lines are angledrelative to the horizontal.

Therefore as interpreted in classical Munsell terms the increasedvividness can be regarded as accompanied by decreased lightness. Anexample appears as the lower, relatively long arrow 315 that anglesoutward and shallowly downward.

At this point, however, a better interpretation requires resorting tothe parameters of the space as defined, rather than as interpreted inMunsell space. In terms of the parameters as defined, parametricindependence is observed strictly and so is quite satisfactory.

The reader may now object that resorting to special definitions in theHSV and HLS systems led to exceedingly undesirable results. Theunfavorability of those results, however, as pointed out earlier aroseprimarily from the unnaturalness and counterintuitiveness of thoseparticular definitions employed--rather than from the use, as such, ofspecial definitions.

In practice, therefore, it is appropriate to evaluate whether thespecial definitions, invoked to permit an interpretation of goodparametric independence, are themselves acceptable. In the HPG model theparameter that departs from the HVC formulation is Fraction-Black K.

That parameter is not derived as a distortion of an intuitively soundvariable (as is the case with "saturation" S in the HSV or HLS systems).It is not a bizarre double-valued function (as in HLS space).

Rather Fraction-Black K arises from a return to first principles andstraightforward definition of an entirely new parameter. It hasintuitive and perceptual integrity in terms of physical addition ofcolorant, to fill a color space--or, alternatively, insertion ofcolorant in place of a fraction of any other colorant (whether chromaticor white).

Consequently designers and end-users of systems using this parameter Kcan be informed of its simple meaning. They will understand readily thata constant amount of black colorant, or constant Fraction-Black K, isdifferent from constant Munsell value V in the following sense.

Holding Fraction-Black K constant does not necessarily impose anyconstraint upon Fraction-White

The latter variable may shift in response to efforts to changeFraction-Colorant N--for the very reason that a quantity of chromaticcolorant is being exchanged for a quantity of white colorant.

Holding V constant implies holding both black and white unchanged inrelative amount, so that their proportions or their ratio remainsstatic.

Thus individuals who are willing to understand what this new variablesignifies will find the physical implication entirely satisfactory. Theywill also find the consequent darkening which accompanies increasedsaturation, as shown in FIG. 19, at least intellectually acceptable.

For some users, however, the objective is actually to move to a newposition horizontally displaced from the starting point--in other words,as suggested by the horizontal dashed arrow 314 in FIG. 19, a purechange in vividness without any change in lightness. That maneuver inHPG space is necessarily compound, but can be performed:

(1) without iteration,

(2) without traversing double-valued parameter ranges, and

(3) without encountering any shifts (hidden or otherwise) of controlsensitivity or calibration.

The maneuver proceeds in two independent steps as shown by the doglegpath in FIG. 19. That path corresponds to:

first following a downward-angling constant-K line to obtain the desiredvividness (Fraction-Colorant N)--as shown by the downward-angled arrow315, already discussed; and

then moving vertically upward 316 to the desired point.

The first step 315 includes a vertical component that corresponds togiving up white in exchange for colorant. The second step 316 is arestoration of the desired white component, exchanging black for white.

In neither of these two steps is there any overshoot or undershoot, interms of either vividness or grayness. In this regard the situationcompares very favorably to those of FIGS. 14 and 15.

In FIGS. 18 and 19, all intersections betweeen constant-K and constant-Nlines are at the same angle, and the same vertical and horizontalspacings, throughout the diagrams. This means that adjustmentsensitivity and calibration are uniform everywhere in the hue page.

For example, the same adjustments applied to the starting pointrepresented for the upper arrow 315 in FIG. 19, as compared with thelower long angled arrow, will produce literally parallel behavior andlead to the same Fraction-Colorant N (vividness) level as the lowerpath. Similarly in FIG. 18 applying the same amount of adjustment atother points in the hue page will produce the same amount of verticalmovement.

An exception to both these statements arises from the inherentfundamental character of the color space itself: not all possibleamounts of lightness--or black and white colorant--have physicalmeaning. The manner of dealing with these fundamental limitations canmake an enormous difference in the practical usefulness of a colorsystem.

For instance a user may wish to move in a horizontal path from thestarting point of the upper angled arrow in FIG. 19, as shown by theupper horizontal dashed arrow 314'. Regardless of color space employed,such a maneuver is an impossibility because the target point correspondsto colors unavailable using the color-delivery device that correspondsto the hue page--i.e., using the available pigments.

If the desired path extends far enough out of the device hue page topoke through the outer surface of the ideal color solid (FIG. 3), aneven stronger prohibition arises. Such colors literally are not real:they correspond to sensations of which no human eye and brain arecapable, to imaginary colors.

Similar situations arise if a user wishes to extend the vertical-arrowpath 313 in FIG. 18 to and beyond the lower envelope line (K=1 toN=1)--or if a user wishes to move a system in the opposite direction, toand beyond the upper envelope line (K=0). In the Fraction-Colorant Ndirection, a user may wish to extend the lower-arrow path 315 in FIG.19, for example to and beyond the lower envelope line as suggested bythe lower angled arrow 315' and its dashed-line extension 314 in FIG.20.

Logically, since no scale compression or expansion is desired, suchadjustments should be within range of the controls. No system can complywith commands to attain unavailable-color or imaginary-color positions,but every system must respond in some way.

A question then arises what the best response should be, for optimumuser convenience, satisfaction with the resulting color, and confidencein the rationality of the system. Major alternatives may be these:

halt operation at the color-space boundary, and leave it to the user todetermine what adjustment to make next;

halt operation at the color-space boundary, and describe to the userwhat selections of further action are available and their consequences;then leave it to the user to determine what adjustment to make next;

proceed in a logical direction along the boundary, in an attempt toprovide the closest real-color approximation to the user's objective;and

pause progress at the boundary and offer the user an alternative ofstopping, proceeding under system control in a logical direction alongthe boundary, or determining what adjustment to make next.

In each case, the system can be programmed to inform the user, first,that the boundary of available (or real) colors has been reached; and,second, what the system has been instructed to do about it. Some systemdesigners, particularly output-device designers, may not have thisoption, since its implementation would be most natural through anapplications program that is under control of other people.

Some system designers may prefer not to offer such information, on thebasis that users will ascribe the limitation to the particular system inuse, rather than to the fundamental nature of color. Such decisions area matter of design choice.

In preferred embodiments of the present invention the first alternativeis substantially excluded. It would leave most users at sea, withoutsufficient information to devise any reasonable action.

The second and third alternatives are both reasonable and acceptable,having complementary though minor drawbacks. The second essentiallydenies the user the benefit of the system designer's expertise indetermining how to effectuate the next most natural adjustment--the onewhich most users would select if they knew how to go about it.

The third may be perceived as slightly undesirable since the user willfind that a desired adjustment of one parameter is now resulting inadmixture of change in a different parameter. This drawback, however,can be minimal in two different situations:

A system may be designed to offer users only a very limited number ofdiscrete color-control options.

An inordinate amount of special attention may be required to flagsituations in which it is necessary to invoke special methods to dealwith requests, in effect, for unavailable/imaginary colors--and toannounce and explain these to the user.

As already mentioned, a system may be set up to provide to users a clearindication of when special evasive maneuvers have been made, or must bemade, to remain inside the color space.

When this occurs the user can decide to reverse the adjustment, or notto make it.

Thus the fourth alternative may be economic, and best, only when thesystem offers complex enough maneuverability within the color space tojustify such an elaborately interactive capability.

With the foregoing discussion in mind, reference is now made to thelower, long angled-arrow path 315'-317 in FIG. 20. This corresponds to auser's or designer's desire for a longer excursion toward greatervividness that seen in FIG. 19.

Extension of the path to the system boundary is straightforward, asshown by the longer downward-angling segment of the new path. The systemcannot proceed along the dashed-arrow extension 314 of that segment, butthe user/designer wants more vividness.

One natural choice would be to move toward greater vividness along thesystem boundary as shown by the upward-angled arrow segment 317. Thedesired vividness is thus achieved, but at the expense of blackness.

It is helpful to compare the two-segment path with the straight pathrepresented by the upper long arrow 315" in FIG. 20. The total excursionin vividness along the two-segment path is the same as if the maneuverwere begun at a point high enough in the hue page to avoid the systemboundary entirely.

If the tradeoff of blackness for vividness turns out to be perceptuallyrejected, the user/designer may simply reverse the process--or part ofit, if such control is available. This moves the system back to theoriginal desirable blackness, and some lower amount of vividness thanthe maximum desired.

All the increasing-vividness examples discussed so far are applicablewithout any conceptual modification to adjustments that begin very closeto the Fraction-Colorant N≡1 vertex, at far right in the drawings.Naturally no Fraction-Colorant N adjustment range can extend beyond thatvertex into unavailable or imaginary colors; the system response at thatpoint simply stops.

Choices similar to the increasing-vividness examples arise in movingvertically along lines of constant Fraction-Colorant N, as shown by thesegmented arrow 313' near lower left in the drawing. Here an adjustmentis under way to increase 317' the blackness or Fraction-Black K.

The adjustment begins by exchanging 313' white for black, but at thesystem boundary the adjustment cannot proceed in that way because heretoo the trajectory would move into unavailable/imaginary colors. Thereason is that the part of the color space occupied by Fraction-ColorantN is all that remains: here there is no more white to give up.

The path is instead advantageously deflected 317' along the boundarytoward the black K≡1 vertex. Here added Fraction-Black K is bought withsome vividness (Fraction-Colorant N) as currency.

Precisely the same total change of blackness is obtained as if theadjustment were begun at a point further to the left in the diagram. Atthat point, because initial vividness is lower, barterable white isavailable in greater quantity--and consequently a greater range 313" ofblackness adjustment is available.

Once again, if the user/designer esthetically rejects the tradeoff ofvividness for the last increment of blackness, the maneuver (or part ofit, in some systems) can be reversed.

Closely analogous operations occur with vertical movement upward,corresponding to a desire to decrease blackness. When the top K≡0boundary is reached, no more Fraction-Black K remains to deduct, but aperceptually related further adjustment (increased whiteness) isavailable by moving toward the white W≡1 vertex at expense of somevividness.

System operation has now been explored rather fully near the hue-pageboundaries--particularly with regard to practical ways of dealing withfundamental limitations of the color phenomenon. As these explorationsshow, the HPG color space is entirely well behaved throughout.

Although it has limit points W≡1, N≡1, K≡1, these are not singularitiesin the mathematical sense of imposing indeterminacies (and not even inthe practical sense of imposing scale compression) on any variable.Range limitations are imposed only where physically necessary.

g. Computer modeling of practical color space

As mentioned previously all the diagrams of FIGS. 13 through 20represent idealized analyses ignoring the effects of many real-worldfactors--such as, for example, chromatically impure real pigments,nonideal subtractive response, pixel overlap, device position-controlimperfections, etc. Some of these factors vary within the color spacesystematically, and so distort the hue-page structure and accordinglythe operation produced by any system.

All of these effects can be taken into account by computer modeling togive other views of hue-page structures. Such other views are morerealistic, and represent the actual coloration that will result in anyspecific image--requiring compensating factors that are also modelable,and that will result in a better color product than the practicalmodeling might suggest.

With these caveats it is instructive to study FIGS. 21 and 22, whichrepresent computer-generated modeling of realistic implementations ofthe HLS and HPG systems respectively. Both plots of course suggest theeffects of using real pigments, in the retraction of operating limitsinward from the vertices of ideal spaces.

Both also suggest some double-valued behavior near the darkest regionsat lower left. Here presumably gray components of chromatic pigments(and possibly chromatic components of black pigments) introduceperturbations.

Both cases of FIGS. 21 and 22 were produced by modeling of the samecolor-reproducing mechanism, in a nonideal environment. The systemreproduced black by using dots that are much larger than ordinarilyexpected; correspondingly the deposition of black not only increased thedarkness, as expected, but also overlapped with the color dotsdeposited.

The result was to cancel the chroma of the color information. Blacktherefore had the effect of reducing chroma and lightnesssimultaneously.

FIG. 21 clearly reflects the chevron-shaped constant-S structure, andthe convergence of constant-S lines at the top and bottom vertices, asshown in FIGS. 15 and 16. This modeling therefore seems to confirm thatthe HLS system in use is indeed subject to singularities at thesepoints.

It also suggests that a real HLS system--using current selections ofpigments and the like--may be subject to undesirable asymmetry of thevalue scale, in that the constant-S contours are badly crowded below thelightness midplane. This would lead to exaggerated vividness response tovalue V adjustments, and suppressed value V response to vividnessadjustments.

Such adverse effects are actually present and perhaps might be overcometo an extent by other pigmentation selections or modification of controlregimes; the graph could be used to guide such efforts. That sort ofmodification, however, may not ameliorate the constant-S convergences atthe vertices or the associated indeterminacies there.

FIG. 22 analogously reflects for an HPG system the advantageousintersection of constant-K lines with the lower boundary--therebypreventing convergence except where forced by the artificialpigmentation effects mentioned just above. The system as thus modeledwould appear to be free of singularities such as found in the HLS (andHSV) systems.

In addition, however, the modeling suggests that a real color-producingmachine--here too using current selections of pigments etc.--may besubject to undesirable angling of the constant Fraction-Colorant N linesaway from the vertical, and nonparallelism of the lines. These effectswould degrade significantly the parametric independence of the HPG spaceand its uniformity of control sensitivity, respectively.

Such adverse effects are actually present in the equipment and areovercome by the color compensation step. Here the modeling graph canserve to guide such efforts, with some feedback from colorimetrics todetermine the nature of the compensation required or desired.

Significant realignments may be realized in this way throughcompensation. The results show that fundamental performance of the HPGsystem, as to well-behavedness and the like, accords with expectations;such efforts would appear to be worthwhile.

Even in the presence of the nonideal response of FIG. 22, thecolor-compensation state successfully is applied because of thecorrelation advantage of HPG. Color tables provided in an Appendix tothis document are the results of such color compensation in the presenceof nonideal parameters.

h. Conclusion as to HPG

The Hue-Plus-Gray Color Model provides several advantages and solvesnumerous prior problems of color control. This summary will include, inpassing, some not mentioned earlier.

HPG provides color control that is accurate and stable, andstraightforwardly implemented in algorithms. It excludes murky colorsfrom the palette, because it excludes distant primaries.

It yields intuititive machine-space color control. It is encodable asgray level and forward to multiple primaries.

It enables avoidance of the drawbacks in prior solutions such ascombinatorial color mixing--which produces murky colors and cannot beconverted to RGB. As to color spacing it overcomes problems of colorsthat are too closely grouped (see FIG. 21) and a sparsely filledpalette.

Relative to HLS space it eliminates the problem of perceptuallyuncorrelated lightness and saturation, and inefficient coding ofsaturation. Relative to RGB it eliminates inefficient color coordinates,perceptually inconsistent color ordering, and poor interpolation.

4. THE NOVEL ERROR-DIFFUSION METHOD

Certain preferred embodiments of the present invention make use of thesame equations as set forth in the discussion of prior-arterror-diffusion methods. Those equations, however, are applied to adifferent assemblage of input information from earlier system stages,and the results used in different ways.

In particular the preferred embodiment keeps track of accumulated errorfor a larger group of colorants--corresponding substantially to a fullspecification of color needed to guide each pixel-printing decision. Thepreferred embodiment in particular keeps track of enough colorants tomaintain identification of the user's desired input color, and employsthat information to constrain the printing decision actively.

Even more specifically, in the preferred embodiment this identificationis performed and maintained in a perceptual space, so that the user'sperceptual expectations are realized directly in perceptual terms. Theperceptual space utilized is the HPG space discussed above.

The system performs its decision-making processes for each pixellocation in turn. The particular location on which the system isoperating at a given time will be called the "current" pixel.

FIG. 23 illustrates how the process works, in terms of the accumulatorsor memory buffers used along the way. The desired input color for thecurrent pixel is expressed in terms of the HPG components HNK--and morespecifically in terms of the six chromatic and two achromatic colorantstypically employed.

As will be recalled, only two chromatics are used to express any colorin the HPG system. Hence only the dominant and subordinate primaries,and the achromatics black and white, are active for any particular inputcolor--and therefore for the active pixel.

The system adds to the numbers for those four colorants the accumulatederrors from earlier calculations--i. e., pixels that were activepreviously, or in verbal shorthand "earlier" pixels. In general all theother six colorants will have been active in those other calculations;therefore the result in general is an array of not four but eightnumbers for the active pixel.

For example if the desired color at the active pixel is expressed interms of YGK, the active colorants are YGKW--but the accumulated errorsfrom earlier pixels generally will be expressed in terms of RGBCMYKW. Toeffectuate this scheme eight different memory buffers are establishedfor each pixel to which error contributions have been made, and theaccumulated errors physically reside in these buffers.

When these eight-number contributions from earlier pixels are added tothe four numbers for the active pixel, new error numbers for the activepixel will stand in the eight buffers for that pixel. The systemnevertheless keeps track of the identity of the four activecolorants--those which were used to express the input color desired andspecified by the user.

Next the system prints just the one of those active colorants whoseerror composite (desired component plus contributions from earlierpixels) is greatest. Even if one of the buffers for some other colorantcontains a larger number, the system will never print any such "other"colorant; it is required to print one of the active colorants only.

This procedure departs in several respects from prior-art errordiffusion. Decisions are not made in an artificially limited machinespace, divorced from information about the input color--but rather aremade in a perceptual space, the novel HPG space, and are constrained bythe components of the desired input color.

Furthermore decisions for different colorants or hue pages are not madeindependently and then left to the vagaries of color subtraction forimplementation. Rather the overall process for the entire active-pixelinput color is integrated into a single decision.

In addition, the preferred embodiment does not necessarily wait until acolorant reaches some threshold strength--some minimum error size.Rather it prints whichever active colorant has strongest compositeerror.

If two or more colorants have the same maximum composite error, anarbitrary decision is made. Typically the system simply prints whicheverof the ties for first place comes first in some predetermined sequence.

After the decision is made, the system commands printing of the colorwhich it has decided to print. It also adjusts the compositeaccumulation in the active-pixel buffers to reflect the printingdecision, and then distributes the adjusted accumulation to nearbypixels.

The two main steps can be effected in either order: either print-commandfirst and then composite-error adjustment/distribution, or conversely.Analogously the distribution substep might be done after the printcommand is issued, but the adjustment substep before.

In any event, to perform the composite-error adjustment the systemdeducts the quantity one from the buffer for the single active colorantwhich it has decided to print. This step makes clear that the bufferscan and indeed often must hold negative numbers.

Then the system distributes the revised buffer-memory contents to nearbypixels in accordance with a geometric weighting pattern. The preferredembodiment uses the prior-art weights shown in FIG. 12.

Alternatively a system in accordance with the invention can use any of agreat variety of other patterns. These include some previously put intouse or proposed, and still others that may be seen as preferable forparticular purposes.

In some cases when the system prints an active colorant whosepreadjustment total does not happen to be largest, this occasion mayarise because the desired input color for the active pixel happened tobe a relatively isolated choice. It may be a very small feature in alarge field (such as part of a fine-line symbol, e.g. an alphanumericcharacter, superposed on a green background), as requested by a userworking at a display device.

The occasion may arise instead because the processing has reached a partof the image where two relatively large fields of different colors abut.The system response in these two cases differs importantly when theactive pixel later has become an earlier pixel.

In the first instance the system may soon move on past the small featureand so again into the broader background. Then those previously reservedcomposite-error numbers--for the unused or "inactive" six colorants--canbecome an "active" part of an active-pixel calculation.

In other words, the unused error numbers that were scattered into thethen-nearby unprocessed pixels will be added to desired-color numbersfor those later pixels. Those unused numbers that correspond to activecolorants for a later pixel can add to those actives and sum to acomposite error for a colorant that is strongest there--and so isprinted.

In the second instance the system does not soon leave the newer colorsof the relatively large field which it has just entered. The unusederror numbers redistributed from an active pixel near the line ofabutment are relatively small fractional values of the numbers whichthat active pixel received from earlier pixels.

These small numbers are in turn subdivided into still-smaller fractionsof error for redistribution at a later pixel--and then resubdivided yetagain and again. As this process goes on there is a tendency for thenumbers corresponding to colorants that are now in alien territory tobecome very small.

In a sense, whether they become small or not is inconsequential, sincethey cannot be part of a printing decision unless processing laterreaches an image region where the corresponding colorants are active.Nevertheless if that processing contingency does occur they can yetbecome contributors to an active pixel as they never or seldom decayentirely to zero.

As a mechanistic step in the overall process of the preferredembodiment, as in some prior-art systems, the system must determinewhether a selected colorant corresponds directly to a single pigmentwhich the color-delivery device can use. If not, the system at somelevel identifies a plurality--usually exactly two--of the devicepigments for use in constructing the selected colorant.

The system then commands actuation of the associated systemhardware--e.g., pens and drive circuitry--to deliver the selectedcolorant. The combination of an ink, a corresponding pen, an associateddrive circuit etc., or the like, corresponds to the language "separatephysical coloring means" employed in certain of the appended claims.

In the preferred embodiment using HPG space, the separate physicalcoloring means employed by the machine (or in a related sense themachine parameters) correspond one-to-one with elements of theperceptual parameters. That is, a color-delivery device may be usedwhich is capable of CMYK(W), and the elements of the perceptual HPGsystem are RGBCMYK(W). The former correspond directly to the latter--notto all of them, as can be seen, but to certain ones, a subset, of them.

FIG. 24 represents the above-described processing in terms of a firmwareor software flowchart. It will be found self explanatory by thoseskilled in the field of implementing color processing in microprocessorroutines.

It will also be understood that the first block or two may beunnecessary or may require modification. If input color informationarrives expressed in some terms other than RGB, then differentconversions are required; and if it arrives already expressed in HPG, noconversion is required.

5. A NOVEL CLUSTERED-DITHER METHOD

The preferred embodiment includes offering users an alternative methodof halftoning, known as clustered dither. The concept of clustereddither is not new in itself.

Use of this technique with the HPG color model, however, has beenimproved and refined as still another aspect of the invention. Followingis a description of halftoning HPG color using the clustered-dithercell.

a. General halftoning concepts

The area of an image to be rendered is organized as a collection ofpixels oriented in both horizontal and vertical directions. Halftoningis required where the data representing each pixel contain moreinformation than the device pixel is capable of reproducing.

Halftoning reduces the quantity of information to the level required bythe device at each pixel in such a way that the aggregate of reproducedpixels appears to contain substantially the same amount of informationas found in the original pixel data representation before halftoning.

Halftoning requires a rendering decision-making process used to achievethese objectives, coupled with a pattern-placement process suited to theimage area that is being rendered.

Error diffusion, discussed in section 4 above, usually provides betterresults at sharp transitions or small image features. It is oftenproblematic, however, in rendering more-gradual transitions and largerfields.

Problems in such environments are due to interference effects betweenthe mathematics of error diffusion and the geometry of an image--as wellas snowplow-like tracks of a diffusion pattern. Here dithering, such asthe improved method described below, is distinctly favorable.

Clustered dither cells--The pattern created by a clustered dither cellis designed to create the impression when viewing the results, that dotsare formed at specific locations which grow in size as the amount ofcolorant or black is increased. The method of designing the ditherrequires generally that each new dot which is placed near a prior dot bepositioned in such a way that it overlaps with the prior dot.

Dispersed dither cells--Dispersed dither cells, another type of ordereddither, are designed to create the opposite effect, that of placing dotsin unoccupied areas of the dither cell, preventing overlapping withother dots as much as possible, until the whole of the dither cell isfilled with dots.

b. Dither-cell placement during rendering

Dither cells are customarily placed initially in a position where theupper left corner Of the cell corresponds to the upper left corner ofthe image being rendered. This placement causes each dither celllocation to now correspond to specific pixels in the image area coveredby the dither cell.

The color printed by the halftoning process is determined by thecombination of the color of the pixel, and the values of the dither cellthat corresponds to that pixel. Rendering of that area of the image istherefore possible.

The dither cell is now re-placed upon the image by shifting the cell tothe right by the amount which corresponds to the width of the cell. Thisnew placement of the cell covers new image area, but is immediatelyadjacent to the area of the image previously covered.

This part of the image may then be rendered. The dither cell is movedagain and again until the right hand side of the image is reached.

The process continues by returning the dither cell to the left side ofthe image and shifting it downward by the amount which corresponds tothe height of the cell.

The process of the prior five paragraphs is then repeated. When theentire area of the image has been covered and rendered, the ditherplacement process is complete, and so is the rendering process.

c. Halftoning HPG color

Described here is the method of halftoning color data represented in theHue Plus Gray color space using a specific ordered dither called aclustered dither pattern. The pattern of the dither is shown in FIG. 1and is comprised of a collection of numbers ranging from 0 to 255.

HPG color conversion to fractional components--The HPG color tripletconsists of hue, fraction color and fraction black. As describedelsewhere in this document, this triplet is converted into a formconsisting of Fraction-Colorant 1 or Fc1, Fraction-Colorant 2 Fc2,Fraction-Black K and Fraction-White W such that the sum of these valuesis unity. Each of these values is multiplied by 255 to scale HPG to thescale of the clustered-dither pattern of the accompanying table.

                                      TABLE                                       __________________________________________________________________________    16 × 16 Clustered Dither Cell                                           __________________________________________________________________________    1  17 81 223                                                                              255                                                                              239                                                                              111                                                                              52 4  20 84 222                                                                              254                                                                              238                                                                              110                                                                              49                    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                                                                   188                                                                              120                                                                              40 168                                                                              200                                                                              153                              9  25 89 213                                                                              245                                                                              229                                                                              101                                                                              60 12 28 92 216                                                                              248                                                                              232                                                                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                              121                              249                                                                              233                                                                              105                                                                              61 13 29 93 220                                                                              252                                                                              236                                                                              108                                                                              64 16 32 96 217                              67 131                                                                              179                                                                              125                                                                              45 173                                                              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                                                            70 134                                                                              182                                                                              115                              243                                                                              227                                                                              99 55 7  23 87 210                                                                              242                                                                              226                                                                              98 54 6  22 86 211                              75 139                                                                              187                                                                              119                                                                              39 167                       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26 90 214                                                                              246                                                                              230                                                                              102                                                                              59                               43 171                                                                              203                                                                              159                                                                              79 143                                                                              191                                                                              122                                                                              42 170                                                                              202                                                           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     177                                                                              127                                                                              47 175                                                                              207                                                                              148                                                                              68 132                                                                              180                                                                              126                                                                              46 174                                                                              206                                                                              145                              __________________________________________________________________________

HPG color-vector generation--The next step is to construct an HPG ColorVector. The four fractional components are arranged in the followingorder: first is Fraction-Black, second is the Fraction-Colorant which isthe darker of the two, third is the Fraction-Colorant that is thelighter, and fourth is Fraction-White.

This reordered collection of components is identified by the notationsK, FcD, FcL and W respectively, where the numerical values weredetermined by the multiplication step in the paragraph above. Next,several threshold values are calculated thus:

    V1=K

    V2=V1+NcD

    V3=V2+NcL.

FIG. 25 is a diagram of the resulting HPG Color Vector.

The rendering decision--When the dither cell is placed upon a portion ofthe image, the rendering of each image pixel is achieved by comparingthe dither cell's value with the threshold values in the HPG ColorVector for that pixel. The decision process is achieved by testing therelationships indicated below, in the order shown.

If the decision specifies printing, the remaining relationships aredisregarded, and the next pixel is then considered. The decision steps,for each pixel in turn, are:

If the dither cell value is less than or equal to:

1. V1, print black;

2. V2, print the color of NcD;

3. V3, print the color of NcL;

otherwise,

4. print white.

6. OVERALL SYSTEM CONCEPTS AND IMPLEMENTATION

a. An HPG color-reproduction system

In principle there is no need for conversion into HPG, as inputdesired-color information can be formulated by a user in HPG parametersHNK at the outset. Since these parameters are particularly easy tocomprehend and use, their use in the first step of color selection andmodification is natural.

FIG. 26 represents such a system. Color choices and desired adjustmentsare entered 42 at a keyboard console, or using a computer so-called"mouse" input device, or with selector switches or other types ofcontrol--but in any event the parameters under control are substantiallyH, N and K.

Many variant input formats could be used in such a system, such asdirect entry of component elements of the HPG parameters--e.g.,fractional parts of RGBCMYKW. These are not the only possible elementnames in an HPG system, since in purest principle hue and gray can beexpressed simply in numerical terms.

Moreover, other points than RGBCMY about the hue scale can be selectedto serve as primaries, or as integral values 0 through 5. Indeed the HPGsystem does not rest upon use of those particular numerics, but as cannow be appreciated is a far more fundamental construct.

Information developed in the control/selection block 43 proceeds in HPGparameters toward both a display device 31 and (when a printinginstruction is issued) a printing device 73--through respectiveintermediate modules.

The printer signal passes first through an HPG color-compensation block56 that effectively adjusts the levels of H, M and K to account forknown distortions that are expected to arise in the printer. Next thesignal is converted into control signals 72 which must be in a languageor space suitable for driving the printer directly.

As previously mentioned, the preferred printing devices are operated byCMYK signals--and these are nominally a subset of RGBCMYKW. Accordingly,signal conversion 71 for the printer may be regarded as a compression ofthe parameters set.

In the process, as will be recalled, transformations are required toaccount for those chromatic primaries which are absent from the devicecommand set: they are constructed subtractively from those which arepresent. Also it is necessary to make suitable provision for oneachromatic colorant that is delivered, so to speak, by loading paper ofthat color into the printing machine.

The invention contemplates use of other printing types, such asxerographic units, and in any case other colorants than CMYK--eitherinstead of or supplementing the RGB elements. Such other colorants neednot be elements of the HPG primaries in use:

As mentioned previously, orange or some other primary couldadvantageously be added to a printing machine. In the case of addingdisplay colorants not part of the HPG primary set, an element ofexpansion (as well as compression) of the colorant set arises at theinterface module.

The printer 73 also may be an entirely different type of device, astechnical improvements in such devices may permit. Any such printingdevice can be driven from an HPG-space selector and compensator, withsuitable conversion at the interface module as illustrated.

The compensation module that is traversed en route to the lowerinterface module (the printer-compression/expansion block) must nullify,to the extent possible, hue anomalies and other nonlinearities expectedto arise in the compression or expansion. These sources of error are inaddition to those already mentioned that are inherent in the operationof the printer itself.

The display signal 33, similarly, passes first through an HPGcolor-compensation block 45 that effectively adjusts the levels of H, Nand K to compensate for known distortions arising in the display device.Next the signal is converted 32 into control signals which must be in alanguage or space suitable for driving the display directly.

Predominantly used display devices 31 are CRTs, operating from RGBsignals--and RGB is nominally a subset of RGBCMYKW. It may be supposedaccordingly that signal conversion for the display is a relativelysimple compression of parameters, similar to that previously describedfor extracting printing-machine control signals from HPG parameters.

In a very broad sense this is true, but again transformations arerequired to account for colorants absent from the machine command set,etc. At least most CRT devices are not capable of CMYW as independentmachine variables.

Therefore chromatics CMY must be constructed additively from driveinformation coordinates RGB, and black K is approximated by the darkgray of the unilluminated display screen. The extent of achromaticsuppression of the RGB signals--i.e., suppression of those three signalsin common--that is required for suitable use of the dark gray screen isto be controlled by the Fraction-Black variable K.

So far the provisions are analogous to those for the CMYK printingmachine, but somewhat the converse. An additional provision is requiredin conventional CRT units to form white.

That colorant must be additively constructed from equal parts of R, Gand B. The additional common signal required at all three CRT guns toaccomplish this is developed from the white signal W in the HPG system.

Color displays may operate using CRT phosphors other than RGB--eitherinstead of or supplementing the RGB elements. Such other phosphors neednot be elements of the HPG primaries in use, just as orange or someother primary might be added to a printer.

Once again in the case of adding display colorants not part of the HPGprimary set, an element of expansion (as well as compression) arises atthe interface module. The display also may be an entirely different typeof device--for instance an LCD unit--as technical improvements in suchdevices may permit.

Any such display device can be driven from an HPG-space selector andcompensator, with suitable conversion at the interface as illustrated.The compensation module here too must deal with distortions that willarise in the compression or expansion, in addition to those at thedisplay.

Another step, required in the control of present-day printing machinesthough not display units--or at least not those of the CRT type--isrendition or halftoning 62, as shown in FIG. 26. This step does notarise from the pointillistic character of the delivery mechanism, and isnot simply a matter of imposing a raster delivery sequence on the data,as these characteristics are common to both display and printing.

Rendition, rather, serves as the analog of variable intensity inCRT-type displays. It enables production of gradual-looking,smooth-looking variations in hue, Fraction-Colorant andFraction-Black--or, more generally, chromatic and tonal gradations.

Most computer-controlled printing devices are best operated on the basisof either printing a pixel or not--rather than attempting to print weakand strong dots, or (as in lithographic work) dots of different sizes.Therefore some mechanism similar to halftoning may be required for anycolor-delivery system, displays included, whose operation mostefficiently proceeds on substantially a go/no-go basis.

The processes occurring within a rendition module are the expression ofrelationships between the specific or unique image specified by auser--in terms of shapes and coloration--and the geometry of thedelivery system. Therefore, in general, they cannot be worked out inadvance for all images and instead are necessarily performed in realtime.

As a practical matter, the various blocks illustrated may be distributedin various ways between, ordinarily, an applications program in the formof desktop-computer software and final processing steps in the form ofprinting-machine firmware. Commonly compensation and the conversionsleading to it, and to the display, are embodied in the software (orpartially embodied as firmware at the display); while rendition and theconversions to print commands are embodied in the firmware.

Such an allocation of functions is practical for most cases, sincedesktop computers generally have limited capability to perform parallelprocessing. Such capability as is present may not be readily invoked tohandle both compensation and rendition procedures simultaneously.

With further development of the present trend toward parallelcapabilities in desktop machines, future systems may provide forhalftoning decisions within the computer software--and in someperceptual language, integrated with the color-compensation stage. Forthe present, however, such a development does not appear to have beenattempted.

One integration which is feasible, however, is to move the compensationinto the firmware with the rendition stage.

FIG. 26 also accounts for two important enhancements of printing-systemperformance that are facilitated by the present invention. Theseenhancements arise as solutions to two kinds of problems:

First, printed pigments interact differently with different types ofsheet medium--such as, for instance, plain paper, glossy paper, specialpaper such as draftsman's translucent vellum, and plastic sheeting usedfor transparencies. Printing on different media therefore distinctlyinfluences the resulting perceived color.

Second, printing different types of images is best effectuated withcorrespondingly different rendition procedures--such as, for instance,error diffusion, clustered dither, and dispersed dither. Some reasonsfor this have been mentioned in section 5-a above; and other systems(such as perhaps dispersed dither) may be in demand as a practicalmatter simply because they have established a following.

Accordingly FIG. 26 shows symbolically how color-compensation proceduresshould be made selectable 54 to take into account the effects ofdifferent media, and rendition procedures should be made selectable63-64 to take into account the effects of different images. To an extenteach of these selections may be made automatically, in response tomachine determinations of the medium type and image character at hand;however, the invention also contemplates user selection of either orboth--either through machine controls or computer commands.

Furthermore color-compensation corrections are necessary for differentrendition selections. This is symbolized in FIG. 26 by use of severalsignal lines 61 from the compensation module to the renditionmodule--corresponding to the several distinct halftoning selectionsindicated below.

b. An HPG color-reproduction subsystem driven by an RGB applicationprogram

FIG. 27 represents one step in the direction of a system that iscompatible with color-graphics application programs and delivery-systemarchitectures that already exist now.

Such applications programs typically operate in HSL coordinates--andsome in RGB coordinates--to drive a display unit, typically in RGB.Therefore most systems include a conversion 148 from the color spaceused in selection 143 to that used in display, as illustrated.

In the system shown, the previously discussed problems of parametricindependence and color-modification are simply accepted as givens. Inother words, the relationship between the input and display modules isconsidered to be outside the control of the printing-subsystem designer.

In practice the intrusion of that printout designer into theapplications-program world is ordinarily limited to provision of aprintout-color "driver"--analogous to a printer action table forword-processing programs. Typically the driver is furnished to theapplications-program vendor for inclusion in the applications-programpackage as sold. The applications program will not ordinarily permit theprintout driver to intercede in its communications to the display.

Further, it is necessary to make some assumption about what the useractually wants. In principle it may be logical to assume that the user'sintention is represented by the input color-selection settings, or theresulting signals from the color-control module.

This may sometimes be correct if the user simply seeks some sort ofreplication of a color image provided by someone else--e.g., an imageprepared commercially. In practice, however, usually either the user orsomeone else has made input color settings based on looking at a displayscreen in some system such as represented in the upper part of FIG. 27.

The only signals that have real physical meaning and which have beenevaluated perceptually are therefore the optical data traveling fromjust such a screen to the eye of the user (or someone else). It istherefore reasonable to treat these too as givens.

In short, a user is assumed to have put up on the screen what the userwants. Whatever colors physically appear there, the remainder of thesystem is designed to effectuate.

It is possible that an applications program may include some sort ofcompensation module 145, either in the color-control block 146 orbetween the signal-split point 151 and the display unit. In the formercase the effects of compensation are irrelevant to the printoutdesigner's problem, which is simply to relate what is printed to what ison the screen.

In the latter case, however, the signals going to the printer departfrom those reaching the printout subsystem. In either case the printoutdesigner's driver can operate effectively only if it was prepared totake into account:

whether a compensation module 145 is present (making the printout systemreceive different signals than the display receives), and if so

the detailed working of that module.

As in FIG. 26, the display-to-HPG conversion 158 and thecolor-compensation module 156 are likely to be incorporated into acolor-printout driver--which is loaded into a computer. For somesystems, however, as mentioned in the preceding section the driver canbe included in the printer firmware.

The remainder of the system (at lower right in the drawing) is likely tobe incorporated into the firmware. The FIG. 27 system is still a stepaway from what now appears feasible or at least optimal commercially.

c. HPG color-compensation, rendition and printing subsystems driven andinterfaced in RGB

FIG. 28 moves a half-step in the direction of present feasibility. Ittakes into account the established interfacing architecture of existingsystems.

Many color-generating devices are already purchased and in use. Manymore devices are already basically designed as to basic architecture,and actually working well.

These designs and architectural implementations represent monumental anddifficult undertakings. As a matter of good design practice and businesspractice alike, it is a crucial necessity to evaluate at each stage ofprogress how best to implement advances.

Such evaluation must include whether better promotion of progress in theuseful arts will be achieved through sweeping away old workingenvironments and implementing new concepts more efficiently in newways--or through cautiously embedding the new implementations in theproven working environments. All such decisions must be unsatisfactoryto some degree, whether because of inefficiency in old architectures orrisk in new ones.

A major consideration in such evaluations is the extent to which newimplementations will accommodate field-retrofit, or factoryrefurbishment, of apparatus or applications-software packages already inexistence. In existing systems, as will be recalled from the precedingdiscussion, the interface between the computer and printout subsystemsmost typically falls between the compensation and rendition stages.

Therefore ready retrofit of existing computer-and-software installationscan be achieved by preserving that interfacing, and with it mostpreferably the language transmitted across the interface. All suchconsiderations militate in favor of the practical solution seen in FIG.28.

As can be seen, the computer subsystem thus includes an outputconversion 266 to popular RGB coordinates. At the other side of theinterface 269, the printer system promptly reconverts 267 the receiveddata back into HPG.

As noted earlier, color compensation 256 and the input conversion 258from RGB to HPG take the form of a color driver. The driver is mosttypically loaded into the computer but sometimes instead, to accommodatesome applications-program vendors, included in the printer firmware.

In either case the driver is typically under control of theprinter-subsystem designer. Accordingly the designer has an option ofprogramming the printer firmware to determine for itself whether itsinput signals are coming precompensated (as in FIG. 28) or requirecompensation.

If necessary this may be facilitated by, for example, includingnoncolor-data flags in outputs of the software version of the driver.The firmware can test for these flags to determine whether the arrivingdata are precompensated.

If so, the firmware then can decide to route the input data directly tothe rendition stage 262; and if not, then through an internalcompensation block first. Such tactics enable production of a machine injust one model, to accommodate either type of applications programautomatically.

If preferred the decision can be effectuated in other ways--including,for example, use of a plug-in compatibility module, and manual switchingof a built-in module. These can be set up to accommodate differentapplications programs in which a driver may be either present or absent.

As in FIG. 27, the compensation block here preferably operates to takeinto account color distortions occurring in interpretation of RGBsignals by the display--as well as those introduced in the renditionsystem, at the printer, and in the several conversion blocks shown alongthe way.

FIG. 28 also reflects an additional practical necessity that arises inseparating the computer and printer subsystems along the typicalboundary that appears lower in the drawing. Rendition selections 263,particularly if made only in the printer subsystem, may have to beconveyed back upstream to the computer subsystem--in order to effectuatethe corresponding necessary selection of color-compensation numbers.

In any event, switching or control of the compensation and renditionstages must be coordinated to maintain correspondence betweencompensation arithmetic and rendition method. FIG. 28 symbolizes thisnecessity as duplicate selector switches 258, 268:

One 258 is just before HPG compensator-output conversion to RGB; theother 268 is just after RGB rendition-input conversion back to HPG. Asbefore, these selections may actually be made by computer commands, andmay be entered by a user or established automatically by the system.

d. RGB-interfaced HPG compensation, rendition and printing withselectable halftoning, sheet medium and vividness

FIG. 29 represents the embodiment of the invention which is now mosthighly preferred, particularly in view of the several factors ofpracticality considered above. While preserving the manifold benefits ofthe HPG color model and new dithering methods introduced above, thisembodiment further addresses the difficulty of completingcolor-compensation calculations in real time or on line, with desktopcomputers of the type now predominantly available.

Discussion of this drawing will dwell only upon its points of divergencefrom the previous three figures illustrating preferred embodiments ofthe invention. The first of these is that look-up tables 356,357 havingthe effect of the conversions into and from HPG space, andcolor-compensation intervening operations within that space, have beenput in place at the position of the upper HPG-space block of FIG. 28.

The preparatory steps, plainly performed in HPG space, of constructingthe tables 356, 357 is symbolized by an inner block--presented in dashedlines as it is not performed by the equipment as manufactured anddistributed, or directly as used, but by other instrumentalities and atan earlier time.

The system allows for user selection of different color adjustments orcompensations. As previously mentioned, in the embodiment now mosthighly preferred exactly two different discrete sets of such adjustmentor compensation are made available.

These adjustment sets correspond respectively to printing of color:

(1) as it appears on the display screen, as closely as can be, and

(2) more vividly.

To be specific, the increased vividness in the second selectable setcorresponds to increased Fraction-Colorant N.

For that reason the symbolism of this selection by the "COLOR"-switchhandle 381--and also the user's selection as between the "MORE VIVID"option and the "REPRODUCED" option--have both been placed inside theupper dashed-line HPG-space area of FIG. 29.

The selection ordinarily is made by means of either computer commands oran actual machine control. In any event it is conceptualized asperformed in HPG space.

The actual implementation, however, is applied to RGB signals andproduces more RGB signals. It is therefore here symbolized by switchcontacts 382, 383 that are outside the HPG-space area.

A similar convention has been applied to symbolization 364-364'-364" ofthe compensations applied for use of the equipment with different sheetmedia. Representation of the user's selection process as in or out ofHPG space is somewhat moot, for the following reason.

As presented earlier, error diffusion and clustered dither in accordancewith the present invention are both performed using HPG parameters andtheir elements. Nevertheless, because dithering is a first-order processit is not capable of effectuating or developing the latent advantages ofHPG processing.

Consequently in fact exactly the same numbers, printing decisions, andoutput appearance result from implementing clustered dither in HPG andRGB. Although the algorithmic procedures differ quite significantly,therefore, choosing between them is merely a matter of design choice--oreven at a more pragmatic level, of programming preference.

In the physical embodiment of the invention that has actually beendeveloped for commercialization, that preference happened to be forimplementation in RGB coordinates. Accordingly--but somewhatarbitrarily, since the choice is not material to the operation of theinvention--the dither halftoning functions 362' are shown as outside HPGspace.

Whether the color-compensation table functions are performed in HPG orRGB space makes a nice semantic question, but here is resolved byshowing the tables 356, 357 partially inside and partially outside thatsame upper HPG-space area.

The most-advanced manifestation of this preferred embodiment of theinvention has been collaboratively prepared for use on the McIntosh®computer. It includes selectable rendition methods--the options offeredbeing error diffusion ED, clustered dither CD and dispersed ditherDD--and four selectable media compensations for plain, glossy andspecial paper and transparent plastic sheet PP, GP, SP, XP respectively,as well as the selectable vividness mentioned above. These options cometo a total of twenty-four crosscombinations, and in fact twenty-fourlook-up tables are provided as part of the commercial package ofhardware and software.

Another manifestation has been prepared for use with the IBM-compatibleMicrosoft Windows® system, offering a selection between clustered anddispersed dither, and the same eight crosscombination selections ofmedium and vividness. Here sixteen crosscombinations of options arefound, and that number of look-up tables is commercially provided.

Yet a third manifestation has been prepared by the Software PublishingCorporation for its Harvard Graphics software package, as an adjunct toMicrosoft DOS®, and offers a selection between (1) plain or specialpaper and (2) glossy paper or transparent plastic sheet--with novividness selection. Accordingly two look-up tables are included in thepackage.

These various manifestations considered together offer prospective usersa range of capabilities and tradeoffs, at correspondingly variouscosts--advantageously allowing users to select the capability mostclosely matching both need and resources. Dispersed dither, vellum paperand glossy paper, however, are used relatively rarely and thereforeancillary.

Putting these latter three options aside, then, the remaining fourteenavailable crosscombinations or combinations taken in the aggregate areconsidered to represent the preferred embodiment that is the best modeof practicing the invention and so is most highly preferred.

This document is intended to enable practice of the invention in itsbest mode by a person (or group of people) of ordinary skill in the artof color-reproduction mechanical systems, electronic systems andprogramming systems. The mechanical systems will be described to someextent in the following section, and a full exhibition of the mechanicsand electronics are shortly available for study in the PaintJet® ModelXL300 color printer of the aforementioned Hewlett-Packard Company.

The programming systems are likewise soon available, but are verygenerally conventional except for conversions 367, 371 from RGB to HPG,and from HPG to CMYK (machine) parameters. The RGB→HPG transformation367 is already set forth in an earlier section, and HPG→CMYK 371 is inpart trivial since half of the full HPG element set is identically CMYKand another element W is not printed per se.

The remaining conversions for RGB→CMYK 371 are well known in the art butwill be presented here for completeness. In the first of the followingexpressions, the notation "min" represents the minimum-choice functionrather than the colorant "Min" or its quantity Min introduced earlier.

    K=min(1-R, 1-G, 1-B)

    C=1-R-K

    M=1-G-K

    Y=1-B-K.

With guidance by all of the foregoing, development of thecolor-compensation tables N1, N2 of FIG. 29 can now be carried out verystraightforwardly by color-engineering personnel. Such personnel areable to supply colorimetric, analytical and mathematical techniques andthe like, needed to determine what color adjustments and compensationsshould in fact be implemented; but it is believed that they willencounter no necessity for further inventive effort.

As noted above, however, it is not intended to restrict the benefits ofthe invention to even such intermediate-level (or higher) engineers--butrather to enable full enjoyment of those benefits by people of quiteordinary skill in this field. Accordingly the entire assemblage offourteen tables that enables practice of the present invention in itsbest mode is tendered in the previously mentioned Appendix to thisdocument.

In general input RGB quantities will not coincide with discrete inputentries in the table, but rather in general each input RGB quantity willbe found to lie between two entries, in each of the three sections.Finding suitable intermediate values, between values explicitlyrepresented in any three-dimensional table, is conventional andsometimes called "trilinear interpolation".

7. COLOR-DELIVERY HARDWARE

In the embodiments of the invention that are now most highly preferred,the color-generating machine, or the device for causing the medium toappear colored, is an ink-dispensing document printer. It is mostpreferably of the thermal-inkjet type.

In these embodiments the visible medium is sheet medium that passesthrough the printer, receiving color inks and black ink that the printerdeposits onto the sheet medium to form substantially stable images. Thevisible-light projection comprises reflection from the color inks andfrom the medium; but in the case of transparent plastic sheet medium theprojection further comprises transmission through the medium, and in acase where fluorescent inks are employed the projection also comprisesoptical emissions from the inks.

The separate physical coloring means comprise a first-primary-color inkof a first composition and a second-primary-color ink of a secondcomposition--both inside the printer. The first device-primary meanscomprise:

the first-primary-color ink,

a first electronically operated pen for discharging the ink,

means for controlling the position of the first pen relative to themedium, and

first circuits for actuating the first pen in coordination with theposition-controlling means to discharge the first ink to selectivelyreflect light, from the region, in a first spectral distribution.

Correspondingly the second device-primary means comprise thesecond-primary-color ink of a second composition, a secondelectronically operated pen for discharging the ink, and means forcontrolling the position of the second pen relative to the medium. Thesecond device-primary means also comprise second circuits for actuatingthe second pen in coordination with the position-controlling means todischarge the second ink to selectively reflect light, from the region,in a second spectral distribution.

As pointed out earlier, when the complements or subordinate primariesare needed an alternative definition is invoked allowing one or theother of the device-primary means to be constituted to provide thedesired visual effect by inks, pens etc. operating in pairs.

The gray-scale means comprise black ink of a third composition insidethe printer, a third electronically operated pen for discharging theink, and means for controlling the position of the third pen relative tothe medium. The gray-scale means also include third circuits foractuating the third pen in coordination with the position-controllingmeans to discharge the black ink to absorb light substantially equallyat substantially all visible-light wavelengths.

It will be understood that the elements of the invention as enumeratedabove related to only the active primaries for expressing a particulardesired color. The actual device has at least one other device-primarymeans to complete its capability for general color production.

a. Pen carriage

FIGS. 30 and 31 show how the pen carriage 85 with its individual penholders or bays 91 and pens 96K, 96Y, 96M, 96C is mounted to a pair ofsupport-and-guide rods 94 for extremely precise lateral positioning inscanning across the medium. To propel the carriage 85 very swiftly alongthose rods 94, a metallic carriage-drive cable or strip 95 is securednear the center 93 of the carriage floor.

The carriage-drive cable 95 is an endless metal loop, mounted aboutcapstans (not shown) at the edges of the printer bed (not shown).Forcibly spun about a motor-driven one of the capstans, thecarriage-drive cable 95 shuttles the carriage 85 back and forth acrossthe bed.

A trailing electrical-cable assembly (not shown) attaches at the rightrear corner 86 of the carriage 85. Its electrical wires bring controlsignals to and from all the pens and onboard portions 87 of theircolor-discharge drive circuitry.

Flex circuits 87 interconnect a pen interface 92 at each pen bay 91 withthe trailing cable, and thereby with other control circuitry mountedstationarily elsewhere in the printer case. That control circuitry inturn is actuated by the rendition and compensation systems discussedearlier.

Just out of sight near the right-front corner of the carriage is aprinted-circuit assembly 88 for a sensor that detects the edge of thesheet medium. That printed-circuit assembly is hidden by a smalloutboard projection 89 which (for reasons clear to those acquainted withSan Francisco) is sometimes familiarly called the "cliffhouse".

Through the cliffhouse 89 extends a so-called "codestrip" (not shown),which bears a pattern of extremely fine optical orifices. The codestrip,stationary relative to the printer bed, serves as a positional referencefor the moving carriage: sensors in the cliffhouse detect and count offeach orifice that the carriage passes, to continuously monitorcarriage-position very precisely.

b. Pen disposition on the carriage

These drawings also suggest that the pens are staggered in the directionperpendicular to the scan. FIG. 32 bears out the suggestion, showing inexaggerated form the relative positions of the CMYK pens.

This staggering helps to avoid laying down too much ink on the medium ina short time. The excessive undried liquid would otherwise produceaggravated cockle of absorbent media, and bleed of the colorants.

It will be understood that the foregoing disclosure is intended to bemerely exemplary, and not to limit the scope of the invention--which isto be determined by reference to the appended claims.

I claim:
 1. Apparatus, for use with a visible medium, and for use withdesired-color information, in the form of red-, green- and blue-colorantinput data from a color-image source; said apparatus comprising:a devicefor causing such medium to appear colored; means defining amachine-readable reference table of data substantially equivalent to thedata in at least some of the Color Look-Up Tables in this document; aprogrammed information processor for receiving such desired-colorinformation, generating device-control signals for the device, and:(A)selecting values in said reference table that substantially correspondto the red-, green- and blue-colorant input data, (B) finding, in thesame reference table, output red-, green- and blue-colorant outputvalues that correspond to said colorant input data, and (C) expressingthe control signals in a form applicable to control the device; anddevice-control means for receiving the signals, in said form, andapplying them to control the device.
 2. The apparatus of claim 1,wherein:the reference table represents output values for inputdesired-color information in three-dimensional color space; and thevalue-selecting means comprise means for trilinear interpolation betweenvalues explicitly represented in the table.
 3. The apparatus of claim 1,for use by a user who has any one of a plurality of different estheticpreferences of color-adjustment operation, and for use with any one of aplurality of different types of visible medium, and wherein:thedevice-control means comprise means for modifying the control signals toeffect halftoning at the device, using any one of a plurality ofdifferent halftoning styles; the table-defining means comprise means forautomatically identifying with respect to each table what one or morefeatures are incorporated into that table, said one or more featuresbeing members of the group consisting of:choice of a particular estheticpreference of color-adjustment operation, use of the apparatus with aparticular type of visible medium, and use by the device-control meansof a particular halftoning style; the programmed information processorfurther comprises means for choosing, for use by said value-selectingmeans, one reference table from the plurality of tables; and the devicefurther comprises manually operable means for such user's entry of oneor more choices, among the selected features, for implementation by thechoosing means.
 4. Apparatus, for use with a visible medium, and for usewith desired-color information, in the form of red-, green- andblue-colorant input data from a color-image source; said apparatuscomprising:a device for causing such medium to appear colored; meansdefining a machine-readable reference table of data equal to the data inat least some of the Color Look-Up Tables in this document; a programmedinformation processor for receiving such desired-color information,generating device-control signals for the device, and:(A) selectingvalues in said reference table that substantially correspond to thered-, green- and blue-colorant input data, (B) finding, in the samereference table, output red-, green- and blue-colorant output valuesthat correspond to said colorant input data, and (C) expressing thecontrol signals in a form applicable to control the device; anddevice-control means for receiving the signals, in said form, andapplying them to control the device.